Packages and functions

library(ggplot2)
library(plyr)
library(dplyr)
library(car)
library(fitdistrplus)
library(tidyr)
library(tidyverse)
library(ggtext)
library(lme4)
library(lmerTest)
library(emmeans)
library(glmmTMB)
library(ggbreak)
library(nlme)
library(cxr)
library(MASS)
library(mvtnorm)
library(DescTools)
library(phia)
library(performance)
library(DHARMa)
library(effects)
library(cowplot)
library(ggeffects)
library(marginaleffects)
library(ggtext)
library(R2admb)
#library(glmmADMB)
library(Rfast2)
library(gridExtra)
library(RColorBrewer)
library(gamlss)
library(gamlss.dist)
library(gamlss.add)
library(LSAfun)
library(arm)

#install.packages("devtools")
#require(devtools)
#remotes::install_github("RadicalCommEcol/anisoFun")
#pak::pkg_install("RadicalCommEcol/anisoFun")
#library(anisoFun)

theme_ines<-theme(axis.text = element_text(size=14), axis.title = element_text(size=14, face="bold"), legend.text = element_text(size=12), strip.text = element_text(size=14), plot.title = element_text(size=14, face="bold"), panel.grid=element_line(colour="white"), panel.background = element_rect(fill="white") , axis.line = element_line(linewidth = 0.5, linetype = "solid",
                                   colour = "black"), strip.background = element_rect(fill="white"))

save_plot<-function(dir, width=15, height=10, ...){
  ggsave(dir, width = width, height = height, units = c("cm"))
}


Env<-c("No cadmium", "Cadmium")
names(Env)<-c("N", "Cd")

regimeTu<-c("Tu no cadmium", "Tu cadmium")
names(regimeTu)<-c("SR1", "SR2")

regimeTe<-c("Te no cadmium", "Te cadmium")
names(regimeTe)<-c("SR4", "SR5")

colors_comb<-brewer.pal(name = "Spectral", 4)

Importing data and checking

Importing Competitive ability

setwd("./Repository/For_repository/")
getwd()
## [1] "/Volumes/IF/Desktop/Project_manuscript/Coexistence_cadmium/Repository/For_repository"
ca<-read.csv(file = "./Data/CompetitiveAbility Cd_G40_complete.csv", header=TRUE) # cdata from the competitive ability

str(ca) 
## 'data.frame':    3680 obs. of  24 variables:
##  $ Block             : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ Rep               : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ Box               : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ Leaf              : int  3 4 3 4 3 4 3 4 3 4 ...
##  $ Disk              : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ Env               : chr  "N" "N" "Cd" "Cd" ...
##  $ FocalSR           : int  4 4 4 4 4 4 4 4 4 4 ...
##  $ CompSR            : int  NA NA NA NA NA NA NA NA NA NA ...
##  $ Dens              : int  1 1 1 1 2 2 2 2 4 4 ...
##  $ Type              : chr  "INTRA" "INTRA" "INTRA" "INTRA" ...
##  $ Focalfemale       : chr  "Te" "Te" "Te" "Te" ...
##  $ FocalDead         : int  0 0 1 0 1 1 0 0 0 0 ...
##  $ FocalDrowned      : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ FocalMissing      : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ NumbDeadComp      : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ NumberOfEggs      : int  11 21 3 9 15 16 17 11 58 24 ...
##  $ NumberOfEggsBelow : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ TeMales           : int  3 3 0 3 2 5 5 3 8 8 ...
##  $ TeFemales         : int  6 9 2 5 2 10 4 4 9 6 ...
##  $ TeQuiescentfemales: int  0 0 0 0 0 0 3 0 3 4 ...
##  $ TuMales           : int  NA NA NA NA NA NA NA NA NA NA ...
##  $ TuFemales         : int  NA NA NA NA NA NA NA NA NA NA ...
##  $ TuQuiescentfemales: int  NA NA NA NA NA NA NA NA NA NA ...
##  $ Observations      : chr  NA NA NA NA ...
# Summary of the data to be sure that everything is ok!
summary(as.factor(ca$FocalSR))
##    1    2    4    5 
## 1000  800  940  940
ca$Block2<-as.factor(ca$Block)
ca$Rep2<-as.factor(ca$Rep)
ca$Disk2<-as.factor(ca$Disk)
ca$Leaf2<-as.factor(ca$Leaf)
ca$Env2<-as.factor(ca$Env)
ca$FocalSR2<-as.factor(ca$FocalSR)
ca$CompSR2<-as.factor(ca$CompSR)
ca$Type2<-as.factor(ca$Type)
ca$Focal_Female2<-as.factor(ca$Focalfemale)


regimeTu<-c("Tu \ncontrol", "Tu evolved \n in cadmium")
names(regimeTu)<-c("SR1", "SR2")

regimeTe<-c("Te \n control", "Te evolved \n in cadmium")
names(regimeTe)<-c("SR4", "SR5")

Creating columns that are needed

ca$Nr_Focal_Females_Tu_Alive_G0<-sapply(c(1:length(ca$Block)), function(x){
  if(ca$Focalfemale[x]=="Tu"){
    if(ca$Type[x]=="INTRA"){
      a<-ca$Dens[x]-ca$FocalDead[x]-ca$FocalDrowned[x]-ca$FocalMissing[x]
    }else
      a<-1-ca$FocalDead[x]-ca$FocalDrowned[x]-ca$FocalMissing[x]
    
  }else
    a<-NA
})

ca$Nr_Focal_Females_Te_Alive_G0<-sapply(c(1:length(ca$Block)), function(x){
  if(ca$Focalfemale[x]=="Te"){
    if(ca$Type[x]=="INTRA"){
      a<-ca$Dens[x]-ca$FocalDead[x]-ca$FocalDrowned[x]-ca$FocalMissing[x]
    }else
      a<-1-ca$FocalDead[x]-ca$FocalDrowned[x]-ca$FocalMissing[x]
    
  }else
    a<-NA
})


ca$Num_Comp_Tu_Alive_G0<-sapply(c(1:length(ca$Block)), function(x){
  if(ca$Focalfemale[x]=="Te"){
    if(ca$Type[x]=="INTER"){
      a<-ca$Dens[x]-ca$NumbDeadComp[x]-1
    }else
      a<-NA
    
  }else
    a<-NA
})


ca$Num_Comp_Te_Alive_G0<-sapply(c(1:length(ca$Block)), function(x){
  if(ca$Focalfemale[x]=="Tu"){
    if(ca$Type[x]=="INTER"){
      a<-ca$Dens[x]-ca$NumbDeadComp[x]-1
    }else
      a<-NA
    
  }else
    a<-NA
})

ca$Nr_Focal_Females_G0<-sapply(c(1:length(ca$Block)), function(x){
    if(ca$Type[x]=="INTRA"){
      a<-ca$Dens[x]
    }else
      a<-1

})



str(ca)
## 'data.frame':    3680 obs. of  38 variables:
##  $ Block                       : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ Rep                         : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ Box                         : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ Leaf                        : int  3 4 3 4 3 4 3 4 3 4 ...
##  $ Disk                        : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ Env                         : chr  "N" "N" "Cd" "Cd" ...
##  $ FocalSR                     : int  4 4 4 4 4 4 4 4 4 4 ...
##  $ CompSR                      : int  NA NA NA NA NA NA NA NA NA NA ...
##  $ Dens                        : int  1 1 1 1 2 2 2 2 4 4 ...
##  $ Type                        : chr  "INTRA" "INTRA" "INTRA" "INTRA" ...
##  $ Focalfemale                 : chr  "Te" "Te" "Te" "Te" ...
##  $ FocalDead                   : int  0 0 1 0 1 1 0 0 0 0 ...
##  $ FocalDrowned                : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ FocalMissing                : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ NumbDeadComp                : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ NumberOfEggs                : int  11 21 3 9 15 16 17 11 58 24 ...
##  $ NumberOfEggsBelow           : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ TeMales                     : int  3 3 0 3 2 5 5 3 8 8 ...
##  $ TeFemales                   : int  6 9 2 5 2 10 4 4 9 6 ...
##  $ TeQuiescentfemales          : int  0 0 0 0 0 0 3 0 3 4 ...
##  $ TuMales                     : int  NA NA NA NA NA NA NA NA NA NA ...
##  $ TuFemales                   : int  NA NA NA NA NA NA NA NA NA NA ...
##  $ TuQuiescentfemales          : int  NA NA NA NA NA NA NA NA NA NA ...
##  $ Observations                : chr  NA NA NA NA ...
##  $ Block2                      : Factor w/ 4 levels "1","2","3","4": 1 1 1 1 1 1 1 1 1 1 ...
##  $ Rep2                        : Factor w/ 5 levels "1","2","3","4",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ Disk2                       : Factor w/ 16 levels "1","2","3","4",..: 1 2 3 4 5 6 7 8 9 10 ...
##  $ Leaf2                       : Factor w/ 2 levels "3","4": 1 2 1 2 1 2 1 2 1 2 ...
##  $ Env2                        : Factor w/ 2 levels "Cd","N": 2 2 1 1 2 2 1 1 2 2 ...
##  $ FocalSR2                    : Factor w/ 4 levels "1","2","4","5": 3 3 3 3 3 3 3 3 3 3 ...
##  $ CompSR2                     : Factor w/ 4 levels "1","2","4","5": NA NA NA NA NA NA NA NA NA NA ...
##  $ Type2                       : Factor w/ 2 levels "INTER","INTRA": 2 2 2 2 2 2 2 2 2 2 ...
##  $ Focal_Female2               : Factor w/ 2 levels "Te","Tu": 1 1 1 1 1 1 1 1 1 1 ...
##  $ Nr_Focal_Females_Tu_Alive_G0: num  NA NA NA NA NA NA NA NA NA NA ...
##  $ Nr_Focal_Females_Te_Alive_G0: num  1 1 0 1 1 1 2 2 4 4 ...
##  $ Num_Comp_Tu_Alive_G0        : num  NA NA NA NA NA NA NA NA NA NA ...
##  $ Num_Comp_Te_Alive_G0        : num  NA NA NA NA NA NA NA NA NA NA ...
##  $ Nr_Focal_Females_G0         : num  1 1 1 1 2 2 2 2 4 4 ...
summary(ca)
##      Block           Rep             Box           Leaf          Disk       
##  Min.   :1.00   Min.   :1.000   Min.   :1.0   Min.   :3.0   Min.   : 1.000  
##  1st Qu.:2.00   1st Qu.:2.000   1st Qu.:1.0   1st Qu.:3.0   1st Qu.: 4.000  
##  Median :2.00   Median :3.000   Median :2.0   Median :3.5   Median : 7.000  
##  Mean   :2.47   Mean   :3.087   Mean   :1.8   Mean   :3.5   Mean   : 7.326  
##  3rd Qu.:4.00   3rd Qu.:4.000   3rd Qu.:2.0   3rd Qu.:4.0   3rd Qu.:11.000  
##  Max.   :4.00   Max.   :5.000   Max.   :3.0   Max.   :4.0   Max.   :16.000  
##                                                                             
##      Env               FocalSR          CompSR           Dens       
##  Length:3680        Min.   :1.000   Min.   :1.000   Min.   : 1.000  
##  Class :character   1st Qu.:1.000   1st Qu.:1.000   1st Qu.: 2.000  
##  Mode  :character   Median :4.000   Median :3.000   Median : 4.000  
##                     Mean   :3.005   Mean   :2.972   Mean   : 4.886  
##                     3rd Qu.:5.000   3rd Qu.:4.250   3rd Qu.:10.000  
##                     Max.   :5.000   Max.   :5.000   Max.   :10.000  
##                                     NA's   :1520                    
##      Type           Focalfemale          FocalDead       FocalDrowned    
##  Length:3680        Length:3680        Min.   :0.0000   Min.   : 0.0000  
##  Class :character   Class :character   1st Qu.:0.0000   1st Qu.: 0.0000  
##  Mode  :character   Mode  :character   Median :0.0000   Median : 0.0000  
##                                        Mean   :0.2572   Mean   : 0.2082  
##                                        3rd Qu.:0.0000   3rd Qu.: 0.0000  
##                                        Max.   :9.0000   Max.   :10.0000  
##                                        NA's   :111      NA's   :111      
##   FocalMissing     NumbDeadComp     NumberOfEggs    NumberOfEggsBelow
##  Min.   :0.0000   Min.   :0.0000   Min.   :  0.00   Min.   : 0.0000  
##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:  7.00   1st Qu.: 0.0000  
##  Median :0.0000   Median :0.0000   Median : 20.00   Median : 0.0000  
##  Mean   :0.0241   Mean   :0.5479   Mean   : 34.12   Mean   : 0.0642  
##  3rd Qu.:0.0000   3rd Qu.:1.0000   3rd Qu.: 47.00   3rd Qu.: 0.0000  
##  Max.   :3.0000   Max.   :9.0000   Max.   :240.00   Max.   :27.0000  
##  NA's   :111      NA's   :112      NA's   :111      NA's   :113      
##     TeMales          TeFemales      TeQuiescentfemales    TuMales       
##  Min.   :  0.000   Min.   : 0.000   Min.   : 0.00      Min.   :  0.000  
##  1st Qu.:  0.000   1st Qu.: 1.000   1st Qu.: 0.00      1st Qu.:  0.000  
##  Median :  1.000   Median : 3.000   Median : 0.00      Median :  0.000  
##  Mean   :  2.566   Mean   : 7.627   Mean   : 1.69      Mean   :  1.533  
##  3rd Qu.:  3.000   3rd Qu.:10.000   3rd Qu.: 2.00      3rd Qu.:  2.000  
##  Max.   :121.000   Max.   :82.000   Max.   :43.00      Max.   :110.000  
##  NA's   :809       NA's   :808      NA's   :808        NA's   :892      
##    TuFemales      TuQuiescentfemales Observations       Block2   Rep2   
##  Min.   : 0.000   Min.   : 0.0000    Length:3680        1: 832   1:800  
##  1st Qu.: 0.000   1st Qu.: 0.0000    Class :character   2:1248   2:480  
##  Median : 1.000   Median : 0.0000    Mode  :character   3: 640   3:800  
##  Mean   : 2.103   Mean   : 0.9505                       4: 960   4:800  
##  3rd Qu.: 3.000   3rd Qu.: 1.0000                                5:800  
##  Max.   :67.000   Max.   :31.0000                                       
##  NA's   :892      NA's   :892                                           
##      Disk2      Leaf2    Env2      FocalSR2 CompSR2       Type2     
##  1      : 275   3:1840   Cd:1840   1:1000   1   : 600   INTER:2160  
##  2      : 275   4:1840   N :1840   2: 800   2   : 480   INTRA:1520  
##  3      : 275                      4: 940   4   : 540               
##  4      : 275                      5: 940   5   : 540               
##  5      : 275                               NA's:1520               
##  6      : 275                                                       
##  (Other):2030                                                       
##  Focal_Female2 Nr_Focal_Females_Tu_Alive_G0 Nr_Focal_Females_Te_Alive_G0
##  Te:1880       Min.   : 0.000               Min.   :-2.000              
##  Tu:1800       1st Qu.: 1.000               1st Qu.: 1.000              
##                Median : 1.000               Median : 1.000              
##                Mean   : 1.592               Mean   : 2.076              
##                3rd Qu.: 1.000               3rd Qu.: 2.000              
##                Max.   :10.000               Max.   :10.000              
##                NA's   :1922                 NA's   :1869                
##  Num_Comp_Tu_Alive_G0 Num_Comp_Te_Alive_G0 Nr_Focal_Females_G0
##  Min.   :-3.000       Min.   :-1.000       Min.   : 1.000     
##  1st Qu.: 1.000       1st Qu.: 1.000       1st Qu.: 1.000     
##  Median : 2.000       Median : 3.000       Median : 1.000     
##  Mean   : 2.958       Mean   : 3.795       Mean   : 2.342     
##  3rd Qu.: 5.000       3rd Qu.: 7.000       3rd Qu.: 2.000     
##  Max.   : 9.000       Max.   : 9.000       Max.   :10.000     
##  NA's   :2649         NA's   :2617
which(ca$Num_Comp_Te_Alive_G0<0)
## [1] 616
which(ca$Num_Comp_Tu_Alive_G0<0)
## [1] 1160
which(ca$Nr_Focal_Females_Tu_Alive_G0<0)
## integer(0)
which(ca$Nr_Focal_Females_Te_Alive_G0<0)
## [1]  824 3559
ca<-ca[-c(which(ca$Num_Comp_Te_Alive_G0<0),which(ca$Num_Comp_Tu_Alive_G0<0), which(ca$Nr_Focal_Females_Te_Alive_G0<0) ),]

#Creating the columns with the correct number of competitors. For conspecifics its always the same as the density to calculate the growth rate. For heterospecifics its always 1 female with X competitors, and DensFocal2 its also to do the same for the conspecifics 

ca$DensFocal<-sapply(c(1:dim(ca)[1]), function(x){
  if(ca$Type[x]=="INTRA"){
    a<-ca$Dens[x]
  }else if(ca$Type[x]=="INTER"){
    a<-1
  }
  
  a
})

ca$DensComp<-sapply(c(1:dim(ca)[1]), function(x){
  if(ca$Type[x]=="INTRA"){
    a<-0
  }else if(ca$Type[x]=="INTER"){
    a<-ca$Dens[x]-1
  }
  
  a
})

ca$DensFocal2<-sapply(c(1:dim(ca)[1]), function(x){
  if(ca$Type[x]=="INTRA"){
    a<-ca$Dens[x]-1
  }else if(ca$Type[x]=="INTER"){
    a<-1
  }
  
  a
})

ca$DensComp2<-sapply(c(1:dim(ca)[1]), function(x){
  if(ca$Type[x]=="INTRA"){
    a<-ca$Dens[x]-1
  }else if(ca$Type[x]=="INTER"){
    a<-ca$Dens[x]-1
  }
  
  a
})

ca$CompSR3<-sapply(c(1:dim(ca)[1]), function(x){
  if(ca$Type[x]=="INTRA"){
    a<-ca$FocalSR[x]
  }else if(ca$Type[x]=="INTER"){
    a<-ca$CompSR[x]
  }
  
  a
})

ca$CompSR3<-as.factor(ca$CompSR3)

Estimate growth rate

ca[,c("Nr_Focal_Females_G0", "Dens", "Type")]
##      Nr_Focal_Females_G0 Dens  Type
## 1                      1    1 INTRA
## 2                      1    1 INTRA
## 3                      1    1 INTRA
## 4                      1    1 INTRA
## 5                      2    2 INTRA
## 6                      2    2 INTRA
## 7                      2    2 INTRA
## 8                      2    2 INTRA
## 9                      4    4 INTRA
## 10                     4    4 INTRA
## 11                     4    4 INTRA
## 12                     4    4 INTRA
## 13                    10   10 INTRA
## 14                    10   10 INTRA
## 15                    10   10 INTRA
## 16                    10   10 INTRA
## 17                     1    1 INTRA
## 18                     1    1 INTRA
## 19                     1    1 INTRA
## 20                     1    1 INTRA
## 21                     2    2 INTRA
## 22                     2    2 INTRA
## 23                     2    2 INTRA
## 24                     2    2 INTRA
## 25                     4    4 INTRA
## 26                     4    4 INTRA
## 27                     4    4 INTRA
## 28                     4    4 INTRA
## 29                    10   10 INTRA
## 30                    10   10 INTRA
## 31                    10   10 INTRA
## 32                    10   10 INTRA
## 33                     1    1 INTRA
## 34                     1    1 INTRA
## 35                     1    1 INTRA
## 36                     1    1 INTRA
## 37                     2    2 INTRA
## 38                     2    2 INTRA
## 39                     2    2 INTRA
## 40                     2    2 INTRA
## 41                     4    4 INTRA
## 42                     4    4 INTRA
## 43                     4    4 INTRA
## 44                     4    4 INTRA
## 45                    10   10 INTRA
## 46                    10   10 INTRA
## 47                    10   10 INTRA
## 48                    10   10 INTRA
## 49                     1    1 INTRA
## 50                     1    1 INTRA
## 51                     1    1 INTRA
## 52                     1    1 INTRA
## 53                     2    2 INTRA
## 54                     2    2 INTRA
## 55                     2    2 INTRA
## 56                     2    2 INTRA
## 57                     4    4 INTRA
## 58                     4    4 INTRA
## 59                     4    4 INTRA
## 60                     4    4 INTRA
## 61                    10   10 INTRA
## 62                    10   10 INTRA
## 63                    10   10 INTRA
## 64                    10   10 INTRA
## 65                     1    2 INTER
## 66                     1    2 INTER
## 67                     1    2 INTER
## 68                     1    2 INTER
## 69                     1    4 INTER
## 70                     1    4 INTER
## 71                     1    4 INTER
## 72                     1    4 INTER
## 73                     1   10 INTER
## 74                     1   10 INTER
## 75                     1   10 INTER
## 76                     1   10 INTER
## 77                     1    2 INTER
## 78                     1    2 INTER
## 79                     1    2 INTER
## 80                     1    2 INTER
## 81                     1    4 INTER
## 82                     1    4 INTER
## 83                     1    4 INTER
## 84                     1    4 INTER
## 85                     1   10 INTER
## 86                     1   10 INTER
## 87                     1   10 INTER
## 88                     1   10 INTER
## 89                     1    2 INTER
## 90                     1    2 INTER
## 91                     1    2 INTER
## 92                     1    2 INTER
## 93                     1    4 INTER
## 94                     1    4 INTER
## 95                     1    4 INTER
## 96                     1    4 INTER
## 97                     1   10 INTER
## 98                     1   10 INTER
## 99                     1   10 INTER
## 100                    1   10 INTER
## 101                    1    2 INTER
## 102                    1    2 INTER
## 103                    1    2 INTER
## 104                    1    2 INTER
## 105                    1    4 INTER
## 106                    1    4 INTER
## 107                    1    4 INTER
## 108                    1    4 INTER
## 109                    1   10 INTER
## 110                    1   10 INTER
## 111                    1   10 INTER
## 112                    1   10 INTER
## 113                    1    2 INTER
## 114                    1    2 INTER
## 115                    1    2 INTER
## 116                    1    2 INTER
## 117                    1    4 INTER
## 118                    1    4 INTER
## 119                    1    4 INTER
## 120                    1    4 INTER
## 121                    1   10 INTER
## 122                    1   10 INTER
## 123                    1   10 INTER
## 124                    1   10 INTER
## 125                    1    2 INTER
## 126                    1    2 INTER
## 127                    1    2 INTER
## 128                    1    2 INTER
## 129                    1    4 INTER
## 130                    1    4 INTER
## 131                    1    4 INTER
## 132                    1    4 INTER
## 133                    1   10 INTER
## 134                    1   10 INTER
## 135                    1   10 INTER
## 136                    1   10 INTER
## 137                    1    2 INTER
## 138                    1    2 INTER
## 139                    1    2 INTER
## 140                    1    2 INTER
## 141                    1    4 INTER
## 142                    1    4 INTER
## 143                    1    4 INTER
## 144                    1    4 INTER
## 145                    1   10 INTER
## 146                    1   10 INTER
## 147                    1   10 INTER
## 148                    1   10 INTER
## 149                    1    2 INTER
## 150                    1    2 INTER
## 151                    1    2 INTER
## 152                    1    2 INTER
## 153                    1    4 INTER
## 154                    1    4 INTER
## 155                    1    4 INTER
## 156                    1    4 INTER
## 157                    1   10 INTER
## 158                    1   10 INTER
## 159                    1   10 INTER
## 160                    1   10 INTER
## 161                    1    1 INTRA
## 162                    1    1 INTRA
## 163                    1    1 INTRA
## 164                    1    1 INTRA
## 165                    2    2 INTRA
## 166                    2    2 INTRA
## 167                    2    2 INTRA
## 168                    2    2 INTRA
## 169                    4    4 INTRA
## 170                    4    4 INTRA
## 171                    4    4 INTRA
## 172                    4    4 INTRA
## 173                   10   10 INTRA
## 174                   10   10 INTRA
## 175                   10   10 INTRA
## 176                   10   10 INTRA
## 177                    1    1 INTRA
## 178                    1    1 INTRA
## 179                    1    1 INTRA
## 180                    1    1 INTRA
## 181                    2    2 INTRA
## 182                    2    2 INTRA
## 183                    2    2 INTRA
## 184                    2    2 INTRA
## 185                    4    4 INTRA
## 186                    4    4 INTRA
## 187                    4    4 INTRA
## 188                    4    4 INTRA
## 189                   10   10 INTRA
## 190                   10   10 INTRA
## 191                   10   10 INTRA
## 192                   10   10 INTRA
## 193                    1    1 INTRA
## 194                    1    1 INTRA
## 195                    1    1 INTRA
## 196                    1    1 INTRA
## 197                    2    2 INTRA
## 198                    2    2 INTRA
## 199                    2    2 INTRA
## 200                    2    2 INTRA
## 201                    4    4 INTRA
## 202                    4    4 INTRA
## 203                    4    4 INTRA
## 204                    4    4 INTRA
## 205                   10   10 INTRA
## 206                   10   10 INTRA
## 207                   10   10 INTRA
## 208                   10   10 INTRA
## 209                    1    1 INTRA
## 210                    1    1 INTRA
## 211                    1    1 INTRA
## 212                    1    1 INTRA
## 213                    2    2 INTRA
## 214                    2    2 INTRA
## 215                    2    2 INTRA
## 216                    2    2 INTRA
## 217                    4    4 INTRA
## 218                    4    4 INTRA
## 219                    4    4 INTRA
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## 1050                   1    1 INTRA
## 1051                   1    1 INTRA
## 1052                   1    1 INTRA
## 1053                   2    2 INTRA
## 1054                   2    2 INTRA
## 1055                   2    2 INTRA
## 1056                   2    2 INTRA
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## 1058                   4    4 INTRA
## 1059                   4    4 INTRA
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## 1061                  10   10 INTRA
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## 1063                  10   10 INTRA
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## 1075                   4    4 INTRA
## 1076                   4    4 INTRA
## 1077                  10   10 INTRA
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## 1125                   1   10 INTER
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## 1139                   1   10 INTER
## 1140                   1   10 INTER
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## 1161                   1   10 INTER
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## 1167                   1    2 INTER
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## 1173                   1   10 INTER
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## 1177                   1    1 INTRA
## 1178                   1    1 INTRA
## 1179                   1    1 INTRA
## 1180                   1    1 INTRA
## 1181                   2    2 INTRA
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## 1186                   4    4 INTRA
## 1187                   4    4 INTRA
## 1188                   4    4 INTRA
## 1189                  10   10 INTRA
## 1190                  10   10 INTRA
## 1191                  10   10 INTRA
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## 1194                   1    1 INTRA
## 1195                   1    1 INTRA
## 1196                   1    1 INTRA
## 1197                   2    2 INTRA
## 1198                   2    2 INTRA
## 1199                   2    2 INTRA
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## 1202                   4    4 INTRA
## 1203                   4    4 INTRA
## 1204                   4    4 INTRA
## 1205                  10   10 INTRA
## 1206                  10   10 INTRA
## 1207                  10   10 INTRA
## 1208                  10   10 INTRA
## 1209                   1    1 INTRA
## 1210                   1    1 INTRA
## 1211                   1    1 INTRA
## 1212                   1    1 INTRA
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## 1218                   4    4 INTRA
## 1219                   4    4 INTRA
## 1220                   4    4 INTRA
## 1221                  10   10 INTRA
## 1222                  10   10 INTRA
## 1223                  10   10 INTRA
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## 1227                   1    1 INTRA
## 1228                   1    1 INTRA
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## 1231                   2    2 INTRA
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## 1234                   4    4 INTRA
## 1235                   4    4 INTRA
## 1236                   4    4 INTRA
## 1237                  10   10 INTRA
## 1238                  10   10 INTRA
## 1239                  10   10 INTRA
## 1240                  10   10 INTRA
## 1241                   1    2 INTER
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## 1249                   1   10 INTER
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## 1255                   1    2 INTER
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## 1258                   1    4 INTER
## 1259                   1    4 INTER
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## 1261                   1   10 INTER
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## 1263                   1   10 INTER
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## 1273                   1   10 INTER
## 1274                   1   10 INTER
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## 1283                   1    4 INTER
## 1284                   1    4 INTER
## 1285                   1   10 INTER
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## 1291                   1    2 INTER
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## 1295                   1    4 INTER
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## 1297                   1   10 INTER
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## 1299                   1   10 INTER
## 1300                   1   10 INTER
## 1301                   1    2 INTER
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## 1303                   1    2 INTER
## 1304                   1    2 INTER
## 1305                   1    4 INTER
## 1306                   1    4 INTER
## 1307                   1    4 INTER
## 1308                   1    4 INTER
## 1309                   1   10 INTER
## 1310                   1   10 INTER
## 1311                   1   10 INTER
## 1312                   1   10 INTER
## 1313                   1    2 INTER
## 1314                   1    2 INTER
## 1315                   1    2 INTER
## 1316                   1    2 INTER
## 1317                   1    4 INTER
## 1318                   1    4 INTER
## 1319                   1    4 INTER
## 1320                   1    4 INTER
## 1321                   1   10 INTER
## 1322                   1   10 INTER
## 1323                   1   10 INTER
## 1324                   1   10 INTER
## 1325                   1    2 INTER
## 1326                   1    2 INTER
## 1327                   1    2 INTER
## 1328                   1    2 INTER
## 1329                   1    4 INTER
## 1330                   1    4 INTER
## 1331                   1    4 INTER
## 1332                   1    4 INTER
## 1333                   1   10 INTER
## 1334                   1   10 INTER
## 1335                   1   10 INTER
## 1336                   1   10 INTER
## 1337                   1    1 INTRA
## 1338                   1    1 INTRA
## 1339                   1    1 INTRA
## 1340                   1    1 INTRA
## 1341                   2    2 INTRA
## 1342                   2    2 INTRA
## 1343                   2    2 INTRA
## 1344                   2    2 INTRA
## 1345                   4    4 INTRA
## 1346                   4    4 INTRA
## 1347                   4    4 INTRA
## 1348                   4    4 INTRA
## 1349                  10   10 INTRA
## 1350                  10   10 INTRA
## 1351                  10   10 INTRA
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## 1353                   1    1 INTRA
## 1354                   1    1 INTRA
## 1355                   1    1 INTRA
## 1356                   1    1 INTRA
## 1357                   2    2 INTRA
## 1358                   2    2 INTRA
## 1359                   2    2 INTRA
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## 1362                   4    4 INTRA
## 1363                   4    4 INTRA
## 1364                   4    4 INTRA
## 1365                  10   10 INTRA
## 1366                  10   10 INTRA
## 1367                  10   10 INTRA
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## 1369                   1    1 INTRA
## 1370                   1    1 INTRA
## 1371                   1    1 INTRA
## 1372                   1    1 INTRA
## 1373                   2    2 INTRA
## 1374                   2    2 INTRA
## 1375                   2    2 INTRA
## 1376                   2    2 INTRA
## 1377                   4    4 INTRA
## 1378                   4    4 INTRA
## 1379                   4    4 INTRA
## 1380                   4    4 INTRA
## 1381                  10   10 INTRA
## 1382                  10   10 INTRA
## 1383                  10   10 INTRA
## 1384                  10   10 INTRA
## 1385                   1    1 INTRA
## 1386                   1    1 INTRA
## 1387                   1    1 INTRA
## 1388                   1    1 INTRA
## 1389                   2    2 INTRA
## 1390                   2    2 INTRA
## 1391                   2    2 INTRA
## 1392                   2    2 INTRA
## 1393                   4    4 INTRA
## 1394                   4    4 INTRA
## 1395                   4    4 INTRA
## 1396                   4    4 INTRA
## 1397                  10   10 INTRA
## 1398                  10   10 INTRA
## 1399                  10   10 INTRA
## 1400                  10   10 INTRA
## 1401                   1    2 INTER
## 1402                   1    2 INTER
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## 1407                   1    4 INTER
## 1408                   1    4 INTER
## 1409                   1   10 INTER
## 1410                   1   10 INTER
## 1411                   1   10 INTER
## 1412                   1   10 INTER
## 1413                   1    2 INTER
## 1414                   1    2 INTER
## 1415                   1    2 INTER
## 1416                   1    2 INTER
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## 1418                   1    4 INTER
## 1419                   1    4 INTER
## 1420                   1    4 INTER
## 1421                   1   10 INTER
## 1422                   1   10 INTER
## 1423                   1   10 INTER
## 1424                   1   10 INTER
## 1425                   1    2 INTER
## 1426                   1    2 INTER
## 1427                   1    2 INTER
## 1428                   1    2 INTER
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## 1430                   1    4 INTER
## 1431                   1    4 INTER
## 1432                   1    4 INTER
## 1433                   1   10 INTER
## 1434                   1   10 INTER
## 1435                   1   10 INTER
## 1436                   1   10 INTER
## 1437                   1    2 INTER
## 1438                   1    2 INTER
## 1439                   1    2 INTER
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## 1442                   1    4 INTER
## 1443                   1    4 INTER
## 1444                   1    4 INTER
## 1445                   1   10 INTER
## 1446                   1   10 INTER
## 1447                   1   10 INTER
## 1448                   1   10 INTER
## 1449                   1    2 INTER
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## 1451                   1    2 INTER
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## 1455                   1    4 INTER
## 1456                   1    4 INTER
## 1457                   1   10 INTER
## 1458                   1   10 INTER
## 1459                   1   10 INTER
## 1460                   1   10 INTER
## 1461                   1    2 INTER
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## 1463                   1    2 INTER
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## 1469                   1   10 INTER
## 1470                   1   10 INTER
## 1471                   1   10 INTER
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## 1481                   1   10 INTER
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## 1483                   1   10 INTER
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## 1493                   1   10 INTER
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## 1495                   1   10 INTER
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## 1500                   1    2 INTER
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## 1503                   1    4 INTER
## 1504                   1    4 INTER
## 1505                   1   10 INTER
## 1506                   1   10 INTER
## 1507                   1   10 INTER
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## 1509                   1    1 INTRA
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## 1513                   2    2 INTRA
## 1514                   2    2 INTRA
## 1515                   2    2 INTRA
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## 1519                   4    4 INTRA
## 1520                   4    4 INTRA
## 1521                  10   10 INTRA
## 1522                  10   10 INTRA
## 1523                  10   10 INTRA
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## 1525                   1    1 INTRA
## 1526                   1    1 INTRA
## 1527                   1    1 INTRA
## 1528                   1    1 INTRA
## 1529                   2    2 INTRA
## 1530                   2    2 INTRA
## 1531                   2    2 INTRA
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## 1534                   4    4 INTRA
## 1535                   4    4 INTRA
## 1536                   4    4 INTRA
## 1537                  10   10 INTRA
## 1538                  10   10 INTRA
## 1539                  10   10 INTRA
## 1540                  10   10 INTRA
## 1541                   1    1 INTRA
## 1542                   1    1 INTRA
## 1543                   1    1 INTRA
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## 1545                   2    2 INTRA
## 1546                   2    2 INTRA
## 1547                   2    2 INTRA
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## 1550                   4    4 INTRA
## 1551                   4    4 INTRA
## 1552                   4    4 INTRA
## 1553                  10   10 INTRA
## 1554                  10   10 INTRA
## 1555                  10   10 INTRA
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## 1557                   1    2 INTER
## 1558                   1    2 INTER
## 1559                   1    2 INTER
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## 1563                   1    4 INTER
## 1564                   1    4 INTER
## 1565                   1   10 INTER
## 1566                   1   10 INTER
## 1567                   1   10 INTER
## 1568                   1   10 INTER
## 1569                   1    2 INTER
## 1570                   1    2 INTER
## 1571                   1    2 INTER
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## 1573                   1    4 INTER
## 1574                   1    4 INTER
## 1575                   1    4 INTER
## 1576                   1    4 INTER
## 1577                   1   10 INTER
## 1578                   1   10 INTER
## 1579                   1   10 INTER
## 1580                   1   10 INTER
## 1581                   1    2 INTER
## 1582                   1    2 INTER
## 1583                   1    2 INTER
## 1584                   1    2 INTER
## 1585                   1    4 INTER
## 1586                   1    4 INTER
## 1587                   1    4 INTER
## 1588                   1    4 INTER
## 1589                   1   10 INTER
## 1590                   1   10 INTER
## 1591                   1   10 INTER
## 1592                   1   10 INTER
## 1593                   1    2 INTER
## 1594                   1    2 INTER
## 1595                   1    2 INTER
## 1596                   1    2 INTER
## 1597                   1    4 INTER
## 1598                   1    4 INTER
## 1599                   1    4 INTER
## 1600                   1    4 INTER
## 1601                   1   10 INTER
## 1602                   1   10 INTER
## 1603                   1   10 INTER
## 1604                   1   10 INTER
## 1605                   1    2 INTER
## 1606                   1    2 INTER
## 1607                   1    2 INTER
## 1608                   1    2 INTER
## 1609                   1    4 INTER
## 1610                   1    4 INTER
## 1611                   1    4 INTER
## 1612                   1    4 INTER
## 1613                   1   10 INTER
## 1614                   1   10 INTER
## 1615                   1   10 INTER
## 1616                   1   10 INTER
## 1617                   1    2 INTER
## 1618                   1    2 INTER
## 1619                   1    2 INTER
## 1620                   1    2 INTER
## 1621                   1    4 INTER
## 1622                   1    4 INTER
## 1623                   1    4 INTER
## 1624                   1    4 INTER
## 1625                   1   10 INTER
## 1626                   1   10 INTER
## 1627                   1   10 INTER
## 1628                   1   10 INTER
## 1629                   1    1 INTRA
## 1630                   1    1 INTRA
## 1631                   1    1 INTRA
## 1632                   1    1 INTRA
## 1633                   2    2 INTRA
## 1634                   2    2 INTRA
## 1635                   2    2 INTRA
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## 1637                   4    4 INTRA
## 1638                   4    4 INTRA
## 1639                   4    4 INTRA
## 1640                   4    4 INTRA
## 1641                  10   10 INTRA
## 1642                  10   10 INTRA
## 1643                  10   10 INTRA
## 1644                  10   10 INTRA
## 1645                   1    1 INTRA
## 1646                   1    1 INTRA
## 1647                   1    1 INTRA
## 1648                   1    1 INTRA
## 1649                   2    2 INTRA
## 1650                   2    2 INTRA
## 1651                   2    2 INTRA
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## 1654                   4    4 INTRA
## 1655                   4    4 INTRA
## 1656                   4    4 INTRA
## 1657                  10   10 INTRA
## 1658                  10   10 INTRA
## 1659                  10   10 INTRA
## 1660                  10   10 INTRA
## 1661                   1    1 INTRA
## 1662                   1    1 INTRA
## 1663                   1    1 INTRA
## 1664                   1    1 INTRA
## 1665                   2    2 INTRA
## 1666                   2    2 INTRA
## 1667                   2    2 INTRA
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## 1669                   4    4 INTRA
## 1670                   4    4 INTRA
## 1671                   4    4 INTRA
## 1672                   4    4 INTRA
## 1673                  10   10 INTRA
## 1674                  10   10 INTRA
## 1675                  10   10 INTRA
## 1676                  10   10 INTRA
## 1677                   1    2 INTER
## 1678                   1    2 INTER
## 1679                   1    2 INTER
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## 1681                   1    4 INTER
## 1682                   1    4 INTER
## 1683                   1    4 INTER
## 1684                   1    4 INTER
## 1685                   1   10 INTER
## 1686                   1   10 INTER
## 1687                   1   10 INTER
## 1688                   1   10 INTER
## 1689                   1    2 INTER
## 1690                   1    2 INTER
## 1691                   1    2 INTER
## 1692                   1    2 INTER
## 1693                   1    4 INTER
## 1694                   1    4 INTER
## 1695                   1    4 INTER
## 1696                   1    4 INTER
## 1697                   1   10 INTER
## 1698                   1   10 INTER
## 1699                   1   10 INTER
## 1700                   1   10 INTER
## 1701                   1    2 INTER
## 1702                   1    2 INTER
## 1703                   1    2 INTER
## 1704                   1    2 INTER
## 1705                   1    4 INTER
## 1706                   1    4 INTER
## 1707                   1    4 INTER
## 1708                   1    4 INTER
## 1709                   1   10 INTER
## 1710                   1   10 INTER
## 1711                   1   10 INTER
## 1712                   1   10 INTER
## 1713                   1    2 INTER
## 1714                   1    2 INTER
## 1715                   1    2 INTER
## 1716                   1    2 INTER
## 1717                   1    4 INTER
## 1718                   1    4 INTER
## 1719                   1    4 INTER
## 1720                   1    4 INTER
## 1721                   1   10 INTER
## 1722                   1   10 INTER
## 1723                   1   10 INTER
## 1724                   1   10 INTER
## 1725                   1    2 INTER
## 1726                   1    2 INTER
## 1727                   1    2 INTER
## 1728                   1    2 INTER
## 1729                   1    4 INTER
## 1730                   1    4 INTER
## 1731                   1    4 INTER
## 1732                   1    4 INTER
## 1733                   1   10 INTER
## 1734                   1   10 INTER
## 1735                   1   10 INTER
## 1736                   1   10 INTER
## 1737                   1    2 INTER
## 1738                   1    2 INTER
## 1739                   1    2 INTER
## 1740                   1    2 INTER
## 1741                   1    4 INTER
## 1742                   1    4 INTER
## 1743                   1    4 INTER
## 1744                   1    4 INTER
## 1745                   1   10 INTER
## 1746                   1   10 INTER
## 1747                   1   10 INTER
## 1748                   1   10 INTER
## 1749                   1    1 INTRA
## 1750                   1    1 INTRA
## 1751                   1    1 INTRA
## 1752                   1    1 INTRA
## 1753                   2    2 INTRA
## 1754                   2    2 INTRA
## 1755                   2    2 INTRA
## 1756                   2    2 INTRA
## 1757                   4    4 INTRA
## 1758                   4    4 INTRA
## 1759                   4    4 INTRA
## 1760                   4    4 INTRA
## 1761                  10   10 INTRA
## 1762                  10   10 INTRA
## 1763                  10   10 INTRA
## 1764                  10   10 INTRA
## 1765                   1    1 INTRA
## 1766                   1    1 INTRA
## 1767                   1    1 INTRA
## 1768                   1    1 INTRA
## 1769                   2    2 INTRA
## 1770                   2    2 INTRA
## 1771                   2    2 INTRA
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## 1773                   4    4 INTRA
## 1774                   4    4 INTRA
## 1775                   4    4 INTRA
## 1776                   4    4 INTRA
## 1777                  10   10 INTRA
## 1778                  10   10 INTRA
## 1779                  10   10 INTRA
## 1780                  10   10 INTRA
## 1781                   1    1 INTRA
## 1782                   1    1 INTRA
## 1783                   1    1 INTRA
## 1784                   1    1 INTRA
## 1785                   2    2 INTRA
## 1786                   2    2 INTRA
## 1787                   2    2 INTRA
## 1788                   2    2 INTRA
## 1789                   4    4 INTRA
## 1790                   4    4 INTRA
## 1791                   4    4 INTRA
## 1792                   4    4 INTRA
## 1793                  10   10 INTRA
## 1794                  10   10 INTRA
## 1795                  10   10 INTRA
## 1796                  10   10 INTRA
## 1797                   1    2 INTER
## 1798                   1    2 INTER
## 1799                   1    2 INTER
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## 1801                   1    4 INTER
## 1802                   1    4 INTER
## 1803                   1    4 INTER
## 1804                   1    4 INTER
## 1805                   1   10 INTER
## 1806                   1   10 INTER
## 1807                   1   10 INTER
## 1808                   1   10 INTER
## 1809                   1    2 INTER
## 1810                   1    2 INTER
## 1811                   1    2 INTER
## 1812                   1    2 INTER
## 1813                   1    4 INTER
## 1814                   1    4 INTER
## 1815                   1    4 INTER
## 1816                   1    4 INTER
## 1817                   1   10 INTER
## 1818                   1   10 INTER
## 1819                   1   10 INTER
## 1820                   1   10 INTER
## 1821                   1    2 INTER
## 1822                   1    2 INTER
## 1823                   1    2 INTER
## 1824                   1    2 INTER
## 1825                   1    4 INTER
## 1826                   1    4 INTER
## 1827                   1    4 INTER
## 1828                   1    4 INTER
## 1829                   1   10 INTER
## 1830                   1   10 INTER
## 1831                   1   10 INTER
## 1832                   1   10 INTER
## 1833                   1    2 INTER
## 1834                   1    2 INTER
## 1835                   1    2 INTER
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## 2629                  10   10 INTRA
## 2630                  10   10 INTRA
## 2631                  10   10 INTRA
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## 2634                   1    1 INTRA
## 2635                   1    1 INTRA
## 2636                   1    1 INTRA
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## 2642                   4    4 INTRA
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## 2717                   1   10 INTER
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## 2765                  10   10 INTRA
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## 2779                   4    4 INTRA
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## 2798                  10   10 INTRA
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## 2813                  10   10 INTRA
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## 2839                   1   10 INTER
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## 2851                   1   10 INTER
## 2852                   1   10 INTER
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## 2859                   1    4 INTER
## 2860                   1    4 INTER
## 2861                   1   10 INTER
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## 2871                   1    4 INTER
## 2872                   1    4 INTER
## 2873                   1   10 INTER
## 2874                   1   10 INTER
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## 2879                   1    2 INTER
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## 2885                   1   10 INTER
## 2886                   1   10 INTER
## 2887                   1   10 INTER
## 2888                   1   10 INTER
## 2889                   1    2 INTER
## 2890                   1    2 INTER
## 2891                   1    2 INTER
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## 2896                   1    4 INTER
## 2897                   1   10 INTER
## 2898                   1   10 INTER
## 2899                   1   10 INTER
## 2900                   1   10 INTER
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## 2902                   1    2 INTER
## 2903                   1    2 INTER
## 2904                   1    2 INTER
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## 2906                   1    4 INTER
## 2907                   1    4 INTER
## 2908                   1    4 INTER
## 2909                   1   10 INTER
## 2910                   1   10 INTER
## 2911                   1   10 INTER
## 2912                   1   10 INTER
## 2913                   1    2 INTER
## 2914                   1    2 INTER
## 2915                   1    2 INTER
## 2916                   1    2 INTER
## 2917                   1    4 INTER
## 2918                   1    4 INTER
## 2919                   1    4 INTER
## 2920                   1    4 INTER
## 2921                   1   10 INTER
## 2922                   1   10 INTER
## 2923                   1   10 INTER
## 2924                   1   10 INTER
## 2925                   1    2 INTER
## 2926                   1    2 INTER
## 2927                   1    2 INTER
## 2928                   1    2 INTER
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## 2930                   1    4 INTER
## 2931                   1    4 INTER
## 2932                   1    4 INTER
## 2933                   1   10 INTER
## 2934                   1   10 INTER
## 2935                   1   10 INTER
## 2936                   1   10 INTER
## 2937                   1    2 INTER
## 2938                   1    2 INTER
## 2939                   1    2 INTER
## 2940                   1    2 INTER
## 2941                   1    4 INTER
## 2942                   1    4 INTER
## 2943                   1    4 INTER
## 2944                   1    4 INTER
## 2945                   1   10 INTER
## 2946                   1   10 INTER
## 2947                   1   10 INTER
## 2948                   1   10 INTER
## 2949                   1    2 INTER
## 2950                   1    2 INTER
## 2951                   1    2 INTER
## 2952                   1    2 INTER
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## 2954                   1    4 INTER
## 2955                   1    4 INTER
## 2956                   1    4 INTER
## 2957                   1   10 INTER
## 2958                   1   10 INTER
## 2959                   1   10 INTER
## 2960                   1   10 INTER
## 2961                   1    1 INTRA
## 2962                   1    1 INTRA
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## 2965                   2    2 INTRA
## 2966                   2    2 INTRA
## 2967                   2    2 INTRA
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## 2970                   4    4 INTRA
## 2971                   4    4 INTRA
## 2972                   4    4 INTRA
## 2973                  10   10 INTRA
## 2974                  10   10 INTRA
## 2975                  10   10 INTRA
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## 2977                   1    1 INTRA
## 2978                   1    1 INTRA
## 2979                   1    1 INTRA
## 2980                   1    1 INTRA
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## 2982                   2    2 INTRA
## 2983                   2    2 INTRA
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## 2986                   4    4 INTRA
## 2987                   4    4 INTRA
## 2988                   4    4 INTRA
## 2989                  10   10 INTRA
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## 2991                  10   10 INTRA
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## 2994                   1    1 INTRA
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## 2996                   1    1 INTRA
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## 3007                  10   10 INTRA
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## 3009                   1    2 INTER
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## 3015                   1    4 INTER
## 3016                   1    4 INTER
## 3017                   1   10 INTER
## 3018                   1   10 INTER
## 3019                   1   10 INTER
## 3020                   1   10 INTER
## 3021                   1    2 INTER
## 3022                   1    2 INTER
## 3023                   1    2 INTER
## 3024                   1    2 INTER
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## 3026                   1    4 INTER
## 3027                   1    4 INTER
## 3028                   1    4 INTER
## 3029                   1   10 INTER
## 3030                   1   10 INTER
## 3031                   1   10 INTER
## 3032                   1   10 INTER
## 3033                   1    2 INTER
## 3034                   1    2 INTER
## 3035                   1    2 INTER
## 3036                   1    2 INTER
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## 3038                   1    4 INTER
## 3039                   1    4 INTER
## 3040                   1    4 INTER
## 3041                   1   10 INTER
## 3042                   1   10 INTER
## 3043                   1   10 INTER
## 3044                   1   10 INTER
## 3045                   1    1 INTRA
## 3046                   1    1 INTRA
## 3047                   1    1 INTRA
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## 3051                   2    2 INTRA
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## 3057                  10   10 INTRA
## 3058                  10   10 INTRA
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## 3088                   4    4 INTRA
## 3089                  10   10 INTRA
## 3090                  10   10 INTRA
## 3091                  10   10 INTRA
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## 3093                   1    2 INTER
## 3094                   1    2 INTER
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## 3099                   1    4 INTER
## 3100                   1    4 INTER
## 3101                   1   10 INTER
## 3102                   1   10 INTER
## 3103                   1   10 INTER
## 3104                   1   10 INTER
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## 3106                   1    2 INTER
## 3107                   1    2 INTER
## 3108                   1    2 INTER
## 3109                   1    4 INTER
## 3110                   1    4 INTER
## 3111                   1    4 INTER
## 3112                   1    4 INTER
## 3113                   1   10 INTER
## 3114                   1   10 INTER
## 3115                   1   10 INTER
## 3116                   1   10 INTER
## 3117                   1    2 INTER
## 3118                   1    2 INTER
## 3119                   1    2 INTER
## 3120                   1    2 INTER
## 3121                   1    4 INTER
## 3122                   1    4 INTER
## 3123                   1    4 INTER
## 3124                   1    4 INTER
## 3125                   1   10 INTER
## 3126                   1   10 INTER
## 3127                   1   10 INTER
## 3128                   1   10 INTER
## 3129                   1    2 INTER
## 3130                   1    2 INTER
## 3131                   1    2 INTER
## 3132                   1    2 INTER
## 3133                   1    4 INTER
## 3134                   1    4 INTER
## 3135                   1    4 INTER
## 3136                   1    4 INTER
## 3137                   1   10 INTER
## 3138                   1   10 INTER
## 3139                   1   10 INTER
## 3140                   1   10 INTER
## 3141                   1    2 INTER
## 3142                   1    2 INTER
## 3143                   1    2 INTER
## 3144                   1    2 INTER
## 3145                   1    4 INTER
## 3146                   1    4 INTER
## 3147                   1    4 INTER
## 3148                   1    4 INTER
## 3149                   1   10 INTER
## 3150                   1   10 INTER
## 3151                   1   10 INTER
## 3152                   1   10 INTER
## 3153                   1    2 INTER
## 3154                   1    2 INTER
## 3155                   1    2 INTER
## 3156                   1    2 INTER
## 3157                   1    4 INTER
## 3158                   1    4 INTER
## 3159                   1    4 INTER
## 3160                   1    4 INTER
## 3161                   1   10 INTER
## 3162                   1   10 INTER
## 3163                   1   10 INTER
## 3164                   1   10 INTER
## 3165                   1    2 INTER
## 3166                   1    2 INTER
## 3167                   1    2 INTER
## 3168                   1    2 INTER
## 3169                   1    4 INTER
## 3170                   1    4 INTER
## 3171                   1    4 INTER
## 3172                   1    4 INTER
## 3173                   1   10 INTER
## 3174                   1   10 INTER
## 3175                   1   10 INTER
## 3176                   1   10 INTER
## 3177                   1    2 INTER
## 3178                   1    2 INTER
## 3179                   1    2 INTER
## 3180                   1    2 INTER
## 3181                   1    4 INTER
## 3182                   1    4 INTER
## 3183                   1    4 INTER
## 3184                   1    4 INTER
## 3185                   1   10 INTER
## 3186                   1   10 INTER
## 3187                   1   10 INTER
## 3188                   1   10 INTER
## 3189                   1    2 INTER
## 3190                   1    2 INTER
## 3191                   1    2 INTER
## 3192                   1    2 INTER
## 3193                   1    4 INTER
## 3194                   1    4 INTER
## 3195                   1    4 INTER
## 3196                   1    4 INTER
## 3197                   1   10 INTER
## 3198                   1   10 INTER
## 3199                   1   10 INTER
## 3200                   1   10 INTER
## 3201                   1    1 INTRA
## 3202                   1    1 INTRA
## 3203                   1    1 INTRA
## 3204                   1    1 INTRA
## 3205                   2    2 INTRA
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## 3210                   4    4 INTRA
## 3211                   4    4 INTRA
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## 3213                  10   10 INTRA
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## 3229                  10   10 INTRA
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## 3242                   4    4 INTRA
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## 3245                  10   10 INTRA
## 3246                  10   10 INTRA
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## 3249                   1    1 INTRA
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## 3251                   1    1 INTRA
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## 3259                   4    4 INTRA
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## 3261                  10   10 INTRA
## 3262                  10   10 INTRA
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## 3265                   1    1 INTRA
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## 3278                  10   10 INTRA
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## 3291                   4    4 INTRA
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## 3293                  10   10 INTRA
## 3294                  10   10 INTRA
## 3295                  10   10 INTRA
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## 3297                   1    2 INTER
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## 3305                   1   10 INTER
## 3306                   1   10 INTER
## 3307                   1   10 INTER
## 3308                   1   10 INTER
## 3309                   1    2 INTER
## 3310                   1    2 INTER
## 3311                   1    2 INTER
## 3312                   1    2 INTER
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## 3314                   1    4 INTER
## 3315                   1    4 INTER
## 3316                   1    4 INTER
## 3317                   1   10 INTER
## 3318                   1   10 INTER
## 3319                   1   10 INTER
## 3320                   1   10 INTER
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## 3322                   1    2 INTER
## 3323                   1    2 INTER
## 3324                   1    2 INTER
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## 3326                   1    4 INTER
## 3327                   1    4 INTER
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## 3329                   1   10 INTER
## 3330                   1   10 INTER
## 3331                   1   10 INTER
## 3332                   1   10 INTER
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## 3334                   1    2 INTER
## 3335                   1    2 INTER
## 3336                   1    2 INTER
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## 3338                   1    4 INTER
## 3339                   1    4 INTER
## 3340                   1    4 INTER
## 3341                   1   10 INTER
## 3342                   1   10 INTER
## 3343                   1   10 INTER
## 3344                   1   10 INTER
## 3345                   1    2 INTER
## 3346                   1    2 INTER
## 3347                   1    2 INTER
## 3348                   1    2 INTER
## 3349                   1    4 INTER
## 3350                   1    4 INTER
## 3351                   1    4 INTER
## 3352                   1    4 INTER
## 3353                   1   10 INTER
## 3354                   1   10 INTER
## 3355                   1   10 INTER
## 3356                   1   10 INTER
## 3357                   1    2 INTER
## 3358                   1    2 INTER
## 3359                   1    2 INTER
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## 3362                   1    4 INTER
## 3363                   1    4 INTER
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## 3365                   1   10 INTER
## 3366                   1   10 INTER
## 3367                   1   10 INTER
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## 3370                   1    2 INTER
## 3371                   1    2 INTER
## 3372                   1    2 INTER
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## 3374                   1    4 INTER
## 3375                   1    4 INTER
## 3376                   1    4 INTER
## 3377                   1   10 INTER
## 3378                   1   10 INTER
## 3379                   1   10 INTER
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## 3381                   1    2 INTER
## 3382                   1    2 INTER
## 3383                   1    2 INTER
## 3384                   1    2 INTER
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## 3386                   1    4 INTER
## 3387                   1    4 INTER
## 3388                   1    4 INTER
## 3389                   1   10 INTER
## 3390                   1   10 INTER
## 3391                   1   10 INTER
## 3392                   1   10 INTER
## 3393                   1    2 INTER
## 3394                   1    2 INTER
## 3395                   1    2 INTER
## 3396                   1    2 INTER
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## 3398                   1    4 INTER
## 3399                   1    4 INTER
## 3400                   1    4 INTER
## 3401                   1   10 INTER
## 3402                   1   10 INTER
## 3403                   1   10 INTER
## 3404                   1   10 INTER
## 3405                   1    2 INTER
## 3406                   1    2 INTER
## 3407                   1    2 INTER
## 3408                   1    2 INTER
## 3409                   1    4 INTER
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## 3411                   1    4 INTER
## 3412                   1    4 INTER
## 3413                   1   10 INTER
## 3414                   1   10 INTER
## 3415                   1   10 INTER
## 3416                   1   10 INTER
## 3417                   1    2 INTER
## 3418                   1    2 INTER
## 3419                   1    2 INTER
## 3420                   1    2 INTER
## 3421                   1    4 INTER
## 3422                   1    4 INTER
## 3423                   1    4 INTER
## 3424                   1    4 INTER
## 3425                   1   10 INTER
## 3426                   1   10 INTER
## 3427                   1   10 INTER
## 3428                   1   10 INTER
## 3429                   1    2 INTER
## 3430                   1    2 INTER
## 3431                   1    2 INTER
## 3432                   1    2 INTER
## 3433                   1    4 INTER
## 3434                   1    4 INTER
## 3435                   1    4 INTER
## 3436                   1    4 INTER
## 3437                   1   10 INTER
## 3438                   1   10 INTER
## 3439                   1   10 INTER
## 3440                   1   10 INTER
## 3441                   1    2 INTER
## 3442                   1    2 INTER
## 3443                   1    2 INTER
## 3444                   1    2 INTER
## 3445                   1    4 INTER
## 3446                   1    4 INTER
## 3447                   1    4 INTER
## 3448                   1    4 INTER
## 3449                   1   10 INTER
## 3450                   1   10 INTER
## 3451                   1   10 INTER
## 3452                   1   10 INTER
## 3453                   1    2 INTER
## 3454                   1    2 INTER
## 3455                   1    2 INTER
## 3456                   1    2 INTER
## 3457                   1    4 INTER
## 3458                   1    4 INTER
## 3459                   1    4 INTER
## 3460                   1    4 INTER
## 3461                   1   10 INTER
## 3462                   1   10 INTER
## 3463                   1   10 INTER
## 3464                   1   10 INTER
## 3465                   1    2 INTER
## 3466                   1    2 INTER
## 3467                   1    2 INTER
## 3468                   1    2 INTER
## 3469                   1    4 INTER
## 3470                   1    4 INTER
## 3471                   1    4 INTER
## 3472                   1    4 INTER
## 3473                   1   10 INTER
## 3474                   1   10 INTER
## 3475                   1   10 INTER
## 3476                   1   10 INTER
## 3477                   1    1 INTRA
## 3478                   1    1 INTRA
## 3479                   1    1 INTRA
## 3480                   1    1 INTRA
## 3481                   2    2 INTRA
## 3482                   2    2 INTRA
## 3483                   2    2 INTRA
## 3484                   2    2 INTRA
## 3485                   4    4 INTRA
## 3486                   4    4 INTRA
## 3487                   4    4 INTRA
## 3488                   4    4 INTRA
## 3489                  10   10 INTRA
## 3490                  10   10 INTRA
## 3491                  10   10 INTRA
## 3492                  10   10 INTRA
## 3493                   1    1 INTRA
## 3494                   1    1 INTRA
## 3495                   1    1 INTRA
## 3496                   1    1 INTRA
## 3497                   2    2 INTRA
## 3498                   2    2 INTRA
## 3499                   2    2 INTRA
## 3500                   2    2 INTRA
## 3501                   4    4 INTRA
## 3502                   4    4 INTRA
## 3503                   4    4 INTRA
## 3504                   4    4 INTRA
## 3505                  10   10 INTRA
## 3506                  10   10 INTRA
## 3507                  10   10 INTRA
## 3508                  10   10 INTRA
## 3509                   1    1 INTRA
## 3510                   1    1 INTRA
## 3511                   1    1 INTRA
## 3512                   1    1 INTRA
## 3513                   2    2 INTRA
## 3514                   2    2 INTRA
## 3515                   2    2 INTRA
## 3516                   2    2 INTRA
## 3517                   4    4 INTRA
## 3518                   4    4 INTRA
## 3519                   4    4 INTRA
## 3520                   4    4 INTRA
## 3521                  10   10 INTRA
## 3522                  10   10 INTRA
## 3523                  10   10 INTRA
## 3524                  10   10 INTRA
## 3525                   1    2 INTER
## 3526                   1    2 INTER
## 3527                   1    2 INTER
## 3528                   1    2 INTER
## 3529                   1    4 INTER
## 3530                   1    4 INTER
## 3531                   1    4 INTER
## 3532                   1    4 INTER
## 3533                   1   10 INTER
## 3534                   1   10 INTER
## 3535                   1   10 INTER
## 3536                   1   10 INTER
## 3537                   1    2 INTER
## 3538                   1    2 INTER
## 3539                   1    2 INTER
## 3540                   1    2 INTER
## 3541                   1    4 INTER
## 3542                   1    4 INTER
## 3543                   1    4 INTER
## 3544                   1    4 INTER
## 3545                   1   10 INTER
## 3546                   1   10 INTER
## 3547                   1   10 INTER
## 3548                   1   10 INTER
## 3549                   1    2 INTER
## 3550                   1    2 INTER
## 3551                   1    2 INTER
## 3552                   1    2 INTER
## 3553                   1    4 INTER
## 3554                   1    4 INTER
## 3555                   1    4 INTER
## 3556                   1    4 INTER
## 3557                   1   10 INTER
## 3558                   1   10 INTER
## 3560                   1   10 INTER
## 3561                   1    2 INTER
## 3562                   1    2 INTER
## 3563                   1    2 INTER
## 3564                   1    2 INTER
## 3565                   1    4 INTER
## 3566                   1    4 INTER
## 3567                   1    4 INTER
## 3568                   1    4 INTER
## 3569                   1   10 INTER
## 3570                   1   10 INTER
## 3571                   1   10 INTER
## 3572                   1   10 INTER
## 3573                   1    2 INTER
## 3574                   1    2 INTER
## 3575                   1    2 INTER
## 3576                   1    2 INTER
## 3577                   1    4 INTER
## 3578                   1    4 INTER
## 3579                   1    4 INTER
## 3580                   1    4 INTER
## 3581                   1   10 INTER
## 3582                   1   10 INTER
## 3583                   1   10 INTER
## 3584                   1   10 INTER
## 3585                   1    2 INTER
## 3586                   1    2 INTER
## 3587                   1    2 INTER
## 3588                   1    2 INTER
## 3589                   1    4 INTER
## 3590                   1    4 INTER
## 3591                   1    4 INTER
## 3592                   1    4 INTER
## 3593                   1   10 INTER
## 3594                   1   10 INTER
## 3595                   1   10 INTER
## 3596                   1   10 INTER
## 3597                   1    2 INTER
## 3598                   1    2 INTER
## 3599                   1    2 INTER
## 3600                   1    2 INTER
## 3601                   1    4 INTER
## 3602                   1    4 INTER
## 3603                   1    4 INTER
## 3604                   1    4 INTER
## 3605                   1   10 INTER
## 3606                   1   10 INTER
## 3607                   1   10 INTER
## 3608                   1   10 INTER
## 3609                   1    2 INTER
## 3610                   1    2 INTER
## 3611                   1    2 INTER
## 3612                   1    2 INTER
## 3613                   1    4 INTER
## 3614                   1    4 INTER
## 3615                   1    4 INTER
## 3616                   1    4 INTER
## 3617                   1   10 INTER
## 3618                   1   10 INTER
## 3619                   1   10 INTER
## 3620                   1   10 INTER
## 3621                   1    2 INTER
## 3622                   1    2 INTER
## 3623                   1    2 INTER
## 3624                   1    2 INTER
## 3625                   1    4 INTER
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## 3627                   1    4 INTER
## 3628                   1    4 INTER
## 3629                   1   10 INTER
## 3630                   1   10 INTER
## 3631                   1   10 INTER
## 3632                   1   10 INTER
## 3633                   1    1 INTRA
## 3634                   1    1 INTRA
## 3635                   1    1 INTRA
## 3636                   1    1 INTRA
## 3637                   2    2 INTRA
## 3638                   2    2 INTRA
## 3639                   2    2 INTRA
## 3640                   2    2 INTRA
## 3641                   4    4 INTRA
## 3642                   4    4 INTRA
## 3643                   4    4 INTRA
## 3644                   4    4 INTRA
## 3645                  10   10 INTRA
## 3646                  10   10 INTRA
## 3647                  10   10 INTRA
## 3648                  10   10 INTRA
## 3649                   1    1 INTRA
## 3650                   1    1 INTRA
## 3651                   1    1 INTRA
## 3652                   1    1 INTRA
## 3653                   2    2 INTRA
## 3654                   2    2 INTRA
## 3655                   2    2 INTRA
## 3656                   2    2 INTRA
## 3657                   4    4 INTRA
## 3658                   4    4 INTRA
## 3659                   4    4 INTRA
## 3660                   4    4 INTRA
## 3661                  10   10 INTRA
## 3662                  10   10 INTRA
## 3663                  10   10 INTRA
## 3664                  10   10 INTRA
## 3665                   1    1 INTRA
## 3666                   1    1 INTRA
## 3667                   1    1 INTRA
## 3668                   1    1 INTRA
## 3669                   2    2 INTRA
## 3670                   2    2 INTRA
## 3671                   2    2 INTRA
## 3672                   2    2 INTRA
## 3673                   4    4 INTRA
## 3674                   4    4 INTRA
## 3675                   4    4 INTRA
## 3676                   4    4 INTRA
## 3677                  10   10 INTRA
## 3678                  10   10 INTRA
## 3679                  10   10 INTRA
## 3680                  10   10 INTRA
ca$GrowthRateOA<-sapply(c(1:length(ca[,1])), function(x){
  #print(x)
  if(ca$Focal_Female[x]=="Tu"){
    a<-ca$TuFemales[x]/ca$DensFocal[x]
  }else if(ca$Focal_Female[x]=="Te"){
    a<-ca$TeFemales[x]/ca$DensFocal[x]
  }else
    a<-NA
  
  a
})

#Growth rate per day
ca$GrowthRatePD<-sapply(c(1:dim(ca)[1]), function(x){
  #print(x)
  if(ca$Focal_Female[x]=="Tu"){
    a<-(ca$TuFemales[x]/ca$DensFocal[x])/3
  }else if(ca$Focal_Female[x]=="Te"){
    a<-(ca$TeFemales[x]/ca$DensFocal[x])/3
  }else{
    a<-NA}
  
  
  a
})

Importing coexistence

setwd("./Repository/For_repository/")
getwd()
## [1] "/Volumes/IF/Desktop/Project_manuscript/Coexistence_cadmium/Repository/For_repository"
coex_g42<-read.csv("./Data/Coexistence Cd_G42_checked.csv", header=TRUE) # Data from the coexistence experiment

coex_g42$Rep2<-as.factor(coex_g42$Rep)
coex_g42$X1st.pair<-as.factor(coex_g42$X1st_pair)
coex_g42$X2nd.pair<-as.factor(coex_g42$X2nd_pair)
coex_g42$SRTu<-as.factor(coex_g42$SRTu)
coex_g42$SRTe<-as.factor(coex_g42$SRTe)
coex_g42$Box2<-as.factor(coex_g42$Box)

### summary data per leaf (because the leaflets are not attributable)
coex_g42_res<-gather(coex_g42, leaf, females, Leaf_2_Up_Tu:Leaf_5_Down_Te, factor_key=TRUE)
str(coex_g42_res)
## 'data.frame':    43200 obs. of  16 variables:
##  $ Rep         : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ Block1      : int  2 2 2 2 2 2 2 2 2 2 ...
##  $ X1st_pair   : chr  "2.4" "2.4" "2.4" "2.4" ...
##  $ X2nd_pair   : chr  "3.5" "3.5" "3.5" "3.5" ...
##  $ Env         : chr  "water" "water" "water" "water" ...
##  $ Box         : int  6 6 6 6 6 7 7 7 7 7 ...
##  $ SRTu        : Factor w/ 2 levels "Tu1","Tu2": 1 1 1 1 1 1 1 1 1 1 ...
##  $ SRTe        : Factor w/ 2 levels "Te4","Te5": 2 2 2 2 2 2 2 2 2 2 ...
##  $ Leaflet     : int  1 2 3 4 5 1 2 3 4 5 ...
##  $ Observations: chr  NA NA NA NA ...
##  $ Rep2        : Factor w/ 5 levels "1","2","3","4",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ X1st.pair   : Factor w/ 8 levels "2.4","24c","2c4",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ X2nd.pair   : Factor w/ 10 levels "1.4","2.4","24c",..: 5 5 5 5 5 5 5 5 5 5 ...
##  $ Box2        : Factor w/ 10 levels "1","2","3","4",..: 6 6 6 6 6 7 7 7 7 7 ...
##  $ leaf        : Factor w/ 16 levels "Leaf_2_Up_Tu",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ females     : int  0 1 2 NA NA 1 2 0 NA NA ...
coex_g42_res$char<-as.character(coex_g42_res$leaf)

aux4<-as.data.frame(t(as.data.frame(sapply(c(1:length(coex_g42_res$Rep)), function(x){
  a<-strsplit(coex_g42_res$char[x], split="_")[[1]]
  
  c(a[2:4])
}))))

colnames(aux4)<-c("Leaf2", "Direction", "Species")

coex_g42_res<-cbind(coex_g42_res, aux4)

str(coex_g42_res)
## 'data.frame':    43200 obs. of  20 variables:
##  $ Rep         : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ Block1      : int  2 2 2 2 2 2 2 2 2 2 ...
##  $ X1st_pair   : chr  "2.4" "2.4" "2.4" "2.4" ...
##  $ X2nd_pair   : chr  "3.5" "3.5" "3.5" "3.5" ...
##  $ Env         : chr  "water" "water" "water" "water" ...
##  $ Box         : int  6 6 6 6 6 7 7 7 7 7 ...
##  $ SRTu        : Factor w/ 2 levels "Tu1","Tu2": 1 1 1 1 1 1 1 1 1 1 ...
##  $ SRTe        : Factor w/ 2 levels "Te4","Te5": 2 2 2 2 2 2 2 2 2 2 ...
##  $ Leaflet     : int  1 2 3 4 5 1 2 3 4 5 ...
##  $ Observations: chr  NA NA NA NA ...
##  $ Rep2        : Factor w/ 5 levels "1","2","3","4",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ X1st.pair   : Factor w/ 8 levels "2.4","24c","2c4",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ X2nd.pair   : Factor w/ 10 levels "1.4","2.4","24c",..: 5 5 5 5 5 5 5 5 5 5 ...
##  $ Box2        : Factor w/ 10 levels "1","2","3","4",..: 6 6 6 6 6 7 7 7 7 7 ...
##  $ leaf        : Factor w/ 16 levels "Leaf_2_Up_Tu",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ females     : int  0 1 2 NA NA 1 2 0 NA NA ...
##  $ char        : chr  "Leaf_2_Up_Tu" "Leaf_2_Up_Tu" "Leaf_2_Up_Tu" "Leaf_2_Up_Tu" ...
##  $ Leaf2       : chr  "2" "2" "2" "2" ...
##  $ Direction   : chr  "Up" "Up" "Up" "Up" ...
##  $ Species     : chr  "Tu" "Tu" "Tu" "Tu" ...
sum_coex_g42<-coex_g42_res %>%
  group_by(Rep2, SRTu, SRTe, Box2, Leaf2,X1st.pair,X2nd.pair, Direction, Species, Env) %>%
  summarize(av_females=sum(females, na.rm=TRUE))
## `summarise()` has grouped output by 'Rep2', 'SRTu', 'SRTe', 'Box2', 'Leaf2',
## 'X1st.pair', 'X2nd.pair', 'Direction', 'Species'. You can override using the
## `.groups` argument.
sum_coex_g42
## # A tibble: 8,640 × 11
## # Groups:   Rep2, SRTu, SRTe, Box2, Leaf2, X1st.pair, X2nd.pair, Direction,
## #   Species [5,936]
##    Rep2  SRTu  SRTe  Box2  Leaf2 X1st.pair X2nd.pair Direction Species Env      
##    <fct> <fct> <fct> <fct> <chr> <fct>     <fct>     <chr>     <chr>   <chr>    
##  1 1     Tu1   Te4   1     2     2.4       3.5       Down      Te      Cd       
##  2 1     Tu1   Te4   1     2     2.4       3.5       Down      Te      water    
##  3 1     Tu1   Te4   1     2     2.4       3.5       Down      Tu      Cd       
##  4 1     Tu1   Te4   1     2     2.4       3.5       Down      Tu      water    
##  5 1     Tu1   Te4   1     2     2.4       3.5       Up        Te      Cd       
##  6 1     Tu1   Te4   1     2     2.4       3.5       Up        Te      water    
##  7 1     Tu1   Te4   1     2     2.4       3.5       Up        Tu      Cd       
##  8 1     Tu1   Te4   1     2     2.4       3.5       Up        Tu      water    
##  9 1     Tu1   Te4   1     2     24c       3c5       Down      Te      Heteroge…
## 10 1     Tu1   Te4   1     2     24c       3c5       Down      Tu      Heteroge…
## # ℹ 8,630 more rows
## # ℹ 1 more variable: av_females <int>
sum_coex_g42$Direction<-as.factor(sum_coex_g42$Direction)

sum_coex_g42_res<-as.data.frame(spread(sum_coex_g42, key=Species, value=av_females))

sum_coex_g42_res2<-sum_coex_g42_res %>%
  group_by(Rep2, SRTu, SRTe, Box2, Leaf2,X1st.pair,X2nd.pair, Env) %>%
  summarize(av_Te=sum(Te, na.rm=TRUE), av_Tu=sum(Tu, na.rm=TRUE)) %>% as.data.frame()
## `summarise()` has grouped output by 'Rep2', 'SRTu', 'SRTe', 'Box2', 'Leaf2',
## 'X1st.pair', 'X2nd.pair'. You can override using the `.groups` argument.
str(sum_coex_g42_res2)
## 'data.frame':    2160 obs. of  10 variables:
##  $ Rep2     : Factor w/ 5 levels "1","2","3","4",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ SRTu     : Factor w/ 2 levels "Tu1","Tu2": 1 1 1 1 1 1 1 1 1 1 ...
##  $ SRTe     : Factor w/ 2 levels "Te4","Te5": 1 1 1 1 1 1 1 1 1 1 ...
##  $ Box2     : Factor w/ 10 levels "1","2","3","4",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ Leaf2    : chr  "2" "2" "2" "3" ...
##  $ X1st.pair: Factor w/ 8 levels "2.4","24c","2c4",..: 1 1 2 1 1 2 1 1 2 1 ...
##  $ X2nd.pair: Factor w/ 10 levels "1.4","2.4","24c",..: 5 5 7 5 5 7 5 5 7 5 ...
##  $ Env      : chr  "Cd" "water" "Heterogeneous" "Cd" ...
##  $ av_Te    : int  85 0 0 90 0 0 18 6 0 206 ...
##  $ av_Tu    : int  11 1 0 2 1 0 0 7 0 22 ...
sum_coex_g42_res2<-sum_coex_g42_res2[-which(sum_coex_g42_res2$Env=="Heterogeneous"),]

coex_g42_rep<-sum_coex_g42_res2 %>%
  group_by(Rep2, Leaf2, SRTu, SRTe, Env, Box2) %>%
  summarize( sum_Te=sum(av_Te, na.rm=TRUE), sum_Tu=mean(av_Tu, na.rm=TRUE)) %>% as.data.frame()
## `summarise()` has grouped output by 'Rep2', 'Leaf2', 'SRTu', 'SRTe', 'Env'. You
## can override using the `.groups` argument.
coex_g42_rep$Env[which(coex_g42_rep$Env=="Cd")]<-"Cd" 

2 - Estimate parameters from cxr package

cxr accepts a data frame with a first column called fitness with positive values and numeric columns with number of individuals. Each row is one individual. For multiple species the easier is to create a list, each with a data frame that has in the first column number of individuals produced and then the number of neighbours

this case we transformed all 0s into 1 (so that the log is 0) For that we need to add +1 to all data so that the variance is not changed.

Note that the files of the output data are available in the folder. To avoid having the run the code again I added eval = FALSE. To use the already generated ouptut files you just need to import the data. To generate the data again, you need to change eval=TRUE.

2.1 - Estimate All replicates together

normal

rows in the alpha element of the returning list correspond to species i and columns to species j for each αij coefficient.

data table summary
Cadmium
data table summary
joining data frame
Importing data files

To use the data sets already available in the repository, we can simply read the csv.

## Importing
param_all_REP<-read.csv("./Analyses/cxr_normal_REP/parameters_cxr_normal_REP.csv")
param_all_REP_upper<-read.csv("./Analyses/cxr_normal_REP/parameters_cxr_normal_REP_upper.csv")
param_all_REP_lower<-read.csv( "./Analyses/cxr_normal_REP/parameters_cxr_normal_REP_lower.csv")
param_all_REP<-param_all_REP[,-1]
param_all_REP_upper<-param_all_REP_upper[,-1]
param_all_REP_lower<-param_all_REP_lower[,-1]

Data wrangling to make it easier to plot the figures

param_all_REP_long<-gather(param_all_REP, parameter, value,Tu_lambda:Te_inter )

param_all_REP_long$category<-mapvalues(param_all_REP_long$parameter, c("Tu_lambda", "Te_lambda", "Tu_intra", "Te_intra","Tu_inter", "Te_inter"), c("lambda", "lambda", "intra", "intra", "inter", "inter"))

param_all_REP_lower_long<-gather(param_all_REP_lower, parameter, value,Tu_lambda:Te_inter )

param_all_REP_lower_long$category<-mapvalues(param_all_REP_lower_long$parameter, c("Tu_lambda", "Te_lambda", "Tu_intra", "Te_intra","Tu_inter", "Te_inter"), c("lambda", "lambda", "intra", "intra", "inter", "inter"))

param_all_REP_upper_long<-gather(param_all_REP_upper, parameter, value,Tu_lambda:Te_inter )

param_all_REP_upper_long$category<-mapvalues(param_all_REP_upper_long$parameter, c("Tu_lambda", "Te_lambda", "Tu_intra", "Te_intra","Tu_inter", "Te_inter"), c("lambda", "lambda", "intra", "intra", "inter", "inter"))

colnames(param_all_REP_lower_long)[5]<-"lower"
colnames(param_all_REP_upper_long)[5]<-"upper"

str(param_all_REP_long)
## 'data.frame':    48 obs. of  6 variables:
##  $ Tu_Regime  : chr  "SR1" "SR2" "SR1" "SR2" ...
##  $ Te_Regime  : chr  "SR4" "SR4" "SR5" "SR5" ...
##  $ Environment: chr  "N" "N" "N" "N" ...
##  $ parameter  : chr  "Tu_lambda" "Tu_lambda" "Tu_lambda" "Tu_lambda" ...
##  $ value      : num  2.48 2.55 2.48 2.55 1.22 ...
##  $ category   : chr  "lambda" "lambda" "lambda" "lambda" ...
param_all_REP_long<-cbind(param_all_REP_long[,1:6],param_all_REP_lower_long$lower, param_all_REP_upper_long$upper)

colnames(param_all_REP_long)[7:8]<-c("lower","upper")

2.2 - Estimate each replicate separately

normal

rows in the alpha element of the returning list correspond to species i and columns to species j for each αij coefficient.

data table summary
Cadmium
data table summary

Again, to use the files already done we can just import from the available files

Importing data files
## Importing
param_all_w0<-read.csv("./Analyses/cxr_normal/parameters_cxr_normal.csv")
param_all_w0_upper<-read.csv("./Analyses/cxr_normal/parameters_cxr_normal_upper.csv")
param_all_w0_lower<-read.csv( "./Analyses/cxr_normal/parameters_cxr_normal_lower.csv")

param_all_w0<-param_all_w0[,-1]
param_all_w0_upper<-param_all_w0_upper[,-1]
param_all_w0_lower<-param_all_w0_lower[,-1]

data wrangling

param_all_w0_long<-gather(param_all_w0, parameter, value,Tu_lambda:Te_inter )

param_all_w0_long$category<-mapvalues(param_all_w0_long$parameter, c("Tu_lambda", "Te_lambda", "Tu_intra", "Te_intra","Tu_inter", "Te_inter"), c("lambda", "lambda", "intra", "intra", "inter", "inter"))

param_all_w0_lower_long<-gather(param_all_w0_lower, parameter, value,Tu_lambda:Te_inter )

param_all_w0_lower_long$category<-mapvalues(param_all_w0_lower_long$parameter, c("Tu_lambda", "Te_lambda", "Tu_intra", "Te_intra","Tu_inter", "Te_inter"), c("lambda", "lambda", "intra", "intra", "inter", "inter"))

param_all_w0_upper_long<-gather(param_all_w0_upper, parameter, value,Tu_lambda:Te_inter )

param_all_w0_upper_long$category<-mapvalues(param_all_w0_upper_long$parameter, c("Tu_lambda", "Te_lambda", "Tu_intra", "Te_intra","Tu_inter", "Te_inter"), c("lambda", "lambda", "intra", "intra", "inter", "inter"))

colnames(param_all_w0_lower_long)[6]<-"lower"
colnames(param_all_w0_upper_long)[6]<-"upper"

str(param_all_w0_long)
## 'data.frame':    216 obs. of  7 variables:
##  $ Tu_Regime  : chr  "SR1" "SR2" "SR1" "SR2" ...
##  $ Te_Regime  : chr  "SR4" "SR4" "SR5" "SR5" ...
##  $ Replicate  : int  1 1 1 1 2 2 3 3 3 3 ...
##  $ Environment: chr  "N" "N" "N" "N" ...
##  $ parameter  : chr  "Tu_lambda" "Tu_lambda" "Tu_lambda" "Tu_lambda" ...
##  $ value      : num  2.52 1.9 2.52 1.9 2.03 ...
##  $ category   : chr  "lambda" "lambda" "lambda" "lambda" ...
param_all_w0_long<-cbind(param_all_w0_long[,1:6],param_all_w0_lower_long$lower, param_all_w0_upper_long$upper)

colnames(param_all_w0_long)[7:8]<-c("lower","upper")
str(param_all_w0_long)
## 'data.frame':    216 obs. of  8 variables:
##  $ Tu_Regime  : chr  "SR1" "SR2" "SR1" "SR2" ...
##  $ Te_Regime  : chr  "SR4" "SR4" "SR5" "SR5" ...
##  $ Replicate  : int  1 1 1 1 2 2 3 3 3 3 ...
##  $ Environment: chr  "N" "N" "N" "N" ...
##  $ parameter  : chr  "Tu_lambda" "Tu_lambda" "Tu_lambda" "Tu_lambda" ...
##  $ value      : num  2.52 1.9 2.52 1.9 2.03 ...
##  $ lower      : num  2.15 1.67 2.15 1.67 1.77 ...
##  $ upper      : num  2.88 2.13 2.88 2.13 2.29 ...

2.3 - Testing differences in parameters (estimated)

2.3.1 - Distribution

str(param_all_w0)
## 'data.frame':    36 obs. of  10 variables:
##  $ Tu_Regime  : chr  "SR1" "SR2" "SR1" "SR2" ...
##  $ Te_Regime  : chr  "SR4" "SR4" "SR5" "SR5" ...
##  $ Replicate  : int  1 1 1 1 2 2 3 3 3 3 ...
##  $ Environment: chr  "N" "N" "N" "N" ...
##  $ Tu_lambda  : num  2.52 1.9 2.52 1.9 2.03 ...
##  $ Te_lambda  : num  4.9 4.9 5.16 5.16 5.12 ...
##  $ Tu_intra   : num  0.05078 -0.01634 0.05078 -0.01634 0.00422 ...
##  $ Te_intra   : num  0.0186 0.0186 0.0419 0.0419 -0.0236 ...
##  $ Tu_inter   : num  0.03981 0.01356 0.04432 0.03235 0.00206 ...
##  $ Te_inter   : num  0.1021 0.0463 0.0591 0.1046 0.2204 ...
descdist(param_all_w0$Tu_lambda, discrete=FALSE, boot=1000)

## summary statistics
## ------
## min:  1.098786   max:  3.512233 
## median:  1.730981 
## mean:  1.935727 
## estimated sd:  0.7423809 
## estimated skewness:  0.6858225 
## estimated kurtosis:  2.336732
descdist(param_all_w0$Te_lambda, discrete=FALSE, boot=1000)

## summary statistics
## ------
## min:  1.363013   max:  8.088399 
## median:  3.140028 
## mean:  3.69777 
## estimated sd:  1.868651 
## estimated skewness:  0.5471405 
## estimated kurtosis:  2.492893
descdist(param_all_w0$Tu_intra, discrete=FALSE, boot=1000)

## summary statistics
## ------
## min:  -0.01664566   max:  0.0776862 
## median:  0.01601209 
## mean:  0.0195158 
## estimated sd:  0.02648953 
## estimated skewness:  0.5018871 
## estimated kurtosis:  2.622023
descdist(param_all_w0$Te_intra, discrete=FALSE, boot=1000)

## summary statistics
## ------
## min:  -0.0236172   max:  0.05467569 
## median:  0.02940243 
## mean:  0.02701788 
## estimated sd:  0.02220119 
## estimated skewness:  -0.6117063 
## estimated kurtosis:  2.445291
descdist(param_all_w0$Tu_inter, discrete=FALSE, boot=1000)

## summary statistics
## ------
## min:  -0.0401219   max:  0.07363919 
## median:  0.0218683 
## mean:  0.02021898 
## estimated sd:  0.02804374 
## estimated skewness:  -0.05890052 
## estimated kurtosis:  2.576286
descdist(param_all_w0$Te_inter, discrete=FALSE, boot=1000)

## summary statistics
## ------
## min:  -0.05584114   max:  0.3147787 
## median:  0.04266622 
## mean:  0.04939625 
## estimated sd:  0.070847 
## estimated skewness:  1.784989 
## estimated kurtosis:  8.103329
hist(param_all_w0$Te_lambda)

hist(param_all_w0$Tu_intra)

hist(param_all_w0$Te_intra)

hist(param_all_w0$Tu_inter)

hist(param_all_w0$Te_inter)

2.3.2 - Does cadmium change parameters?

gr_tu_cd_1<-glmmTMB(Tu_lambda~Environment, data=subset(param_all_w0, Tu_Regime=="SR1" & Te_Regime=="SR4" ))
gr_tu_cd_2<-glmmTMB(Tu_lambda~Environment, data=subset(param_all_w0, Tu_Regime=="SR1" & Te_Regime=="SR4" ), family=Gamma(link="log"))
gr_tu_cd_3<-glmmTMB(Tu_lambda~Environment, data=subset(param_all_w0, Tu_Regime=="SR1" & Te_Regime=="SR4" ), family=gaussian(link="log"))
anova(gr_tu_cd_1,gr_tu_cd_2,gr_tu_cd_3)
## Data: subset(param_all_w0, Tu_Regime == "SR1" & Te_Regime == "SR4")
## Models:
## gr_tu_cd_1: Tu_lambda ~ Environment, zi=~0, disp=~1
## gr_tu_cd_2: Tu_lambda ~ Environment, zi=~0, disp=~1
## gr_tu_cd_3: Tu_lambda ~ Environment, zi=~0, disp=~1
##            Df     AIC     BIC   logLik deviance  Chisq Chi Df Pr(>Chisq)    
## gr_tu_cd_1  3 11.5117 12.4194 -2.75584   5.5117                             
## gr_tu_cd_2  3  5.3421  6.2499  0.32893  -0.6579 6.1695      0     <2e-16 ***
## gr_tu_cd_3  3 11.5117 12.4194 -2.75584   5.5117 0.0000      0          1    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(gr_tu_cd_2)
##  Family: Gamma  ( log )
## Formula:          Tu_lambda ~ Environment
## Data: subset(param_all_w0, Tu_Regime == "SR1" & Te_Regime == "SR4")
## 
##      AIC      BIC   logLik deviance df.resid 
##      5.3      6.2      0.3     -0.7        7 
## 
## 
## Dispersion estimate for Gamma family (sigma^2): 0.0181 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)    0.2006     0.0601   3.338 0.000844 ***
## EnvironmentN   0.7211     0.0850   8.484  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
simulationOutput <- simulateResiduals(fittedModel = gr_tu_cd_2, plot = F)
plot(simulationOutput)
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.25. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.5. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.75. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.

#No problems

gr_te_cd_1<-glmmTMB(Te_lambda~Environment,  data=subset(param_all_w0, Tu_Regime=="SR1" & Te_Regime=="SR4" ))
gr_te_cd_2<-glmmTMB(Te_lambda~Environment,  data=subset(param_all_w0, Tu_Regime=="SR1" & Te_Regime=="SR4" ), family=Gamma(link="log"))
gr_te_cd_3<-glmmTMB(Te_lambda~Environment,  data=subset(param_all_w0, Tu_Regime=="SR1" & Te_Regime=="SR4" ), family=gaussian(link="log"))
anova(gr_te_cd_1,gr_te_cd_2,gr_te_cd_3)
## Data: subset(param_all_w0, Tu_Regime == "SR1" & Te_Regime == "SR4")
## Models:
## gr_te_cd_1: Te_lambda ~ Environment, zi=~0, disp=~1
## gr_te_cd_2: Te_lambda ~ Environment, zi=~0, disp=~1
## gr_te_cd_3: Te_lambda ~ Environment, zi=~0, disp=~1
##            Df    AIC    BIC   logLik deviance  Chisq Chi Df Pr(>Chisq)    
## gr_te_cd_1  3 31.497 32.405 -12.7485   25.497                             
## gr_te_cd_2  3 22.106 23.014  -8.0531   16.106 9.3908      0     <2e-16 ***
## gr_te_cd_3  3 31.497 32.405 -12.7485   25.497 0.0000      0          1    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(gr_te_cd_2)
##  Family: Gamma  ( log )
## Formula:          Te_lambda ~ Environment
## Data: subset(param_all_w0, Tu_Regime == "SR1" & Te_Regime == "SR4")
## 
##      AIC      BIC   logLik deviance df.resid 
##     22.1     23.0     -8.1     16.1        7 
## 
## 
## Dispersion estimate for Gamma family (sigma^2): 0.0298 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)   0.56092    0.07726    7.26 3.87e-13 ***
## EnvironmentN  1.18262    0.10926   10.82  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
simulationOutput <- simulateResiduals(fittedModel = gr_te_cd_2, plot = F)
plot(simulationOutput)# No problems
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.25. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.5. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.75. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.

########

intra_tu_cd_1<-glmmTMB(Tu_intra~Environment,  data=subset(param_all_w0, Tu_Regime=="SR1" & Te_Regime=="SR4" ))
intra_tu_cd_2<-glmmTMB(Tu_intra+1~Environment,  data=subset(param_all_w0, Tu_Regime=="SR1" & Te_Regime=="SR4" ), family=Gamma(link="log"))
intra_tu_cd_3<-glmmTMB(Tu_intra+1~Environment,  data=subset(param_all_w0, Tu_Regime=="SR1" & Te_Regime=="SR4" ), family=gaussian(link="log"))
anova(intra_tu_cd_1,intra_tu_cd_2,intra_tu_cd_3)
## Data: subset(param_all_w0, Tu_Regime == "SR1" & Te_Regime == "SR4")
## Models:
## intra_tu_cd_1: Tu_intra ~ Environment, zi=~0, disp=~1
## intra_tu_cd_2: Tu_intra + 1 ~ Environment, zi=~0, disp=~1
## intra_tu_cd_3: Tu_intra + 1 ~ Environment, zi=~0, disp=~1
##               Df     AIC     BIC logLik deviance  Chisq Chi Df Pr(>Chisq)    
## intra_tu_cd_1  3 -40.051 -39.144 23.026  -46.051                             
## intra_tu_cd_2  3 -40.248 -39.340 23.124  -46.248 0.1966      0     <2e-16 ***
## intra_tu_cd_3  3 -40.051 -39.144 23.026  -46.051 0.0000      0          1    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(intra_tu_cd_1) 
##  Family: gaussian  ( identity )
## Formula:          Tu_intra ~ Environment
## Data: subset(param_all_w0, Tu_Regime == "SR1" & Te_Regime == "SR4")
## 
##      AIC      BIC   logLik deviance df.resid 
##    -40.1    -39.1     23.0    -46.1        7 
## 
## 
## Dispersion estimate for gaussian family (sigma^2): 0.000586 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)
## (Intercept)  0.009066   0.010821   0.838    0.402
## EnvironmentN 0.019251   0.015304   1.258    0.208
summary(intra_tu_cd_2) #### But added +1 to all data
##  Family: Gamma  ( log )
## Formula:          Tu_intra + 1 ~ Environment
## Data: subset(param_all_w0, Tu_Regime == "SR1" & Te_Regime == "SR4")
## 
##      AIC      BIC   logLik deviance df.resid 
##    -40.2    -39.3     23.1    -46.2        7 
## 
## 
## Dispersion estimate for Gamma family (sigma^2): 0.000553 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)
## (Intercept)  0.009025   0.010521   0.858    0.391
## EnvironmentN 0.018898   0.014879   1.270    0.204
simulationOutput <- simulateResiduals(fittedModel = intra_tu_cd_1, plot = F)
plot(simulationOutput)# No problems
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.25. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.5. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.75. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.

#Gamma and gaussian give very similar estimates and values
intra_te_cd_1<-glmmTMB(Te_intra~Environment,  data=subset(param_all_w0, Tu_Regime=="SR1" & Te_Regime=="SR4" ))
intra_te_cd_2<-glmmTMB(Te_intra+1~Environment,  data=subset(param_all_w0, Tu_Regime=="SR1" & Te_Regime=="SR4" ), family=Gamma(link="log"))
intra_te_cd_3<-glmmTMB(Te_intra+1~Environment,  data=subset(param_all_w0, Tu_Regime=="SR1" & Te_Regime=="SR4" ), family=gaussian(link="log"))
anova(intra_te_cd_1,intra_te_cd_2,intra_te_cd_3)
## Data: subset(param_all_w0, Tu_Regime == "SR1" & Te_Regime == "SR4")
## Models:
## intra_te_cd_1: Te_intra ~ Environment, zi=~0, disp=~1
## intra_te_cd_2: Te_intra + 1 ~ Environment, zi=~0, disp=~1
## intra_te_cd_3: Te_intra + 1 ~ Environment, zi=~0, disp=~1
##               Df     AIC     BIC logLik deviance  Chisq Chi Df Pr(>Chisq)    
## intra_te_cd_1  3 -43.086 -42.178 24.543  -49.086                             
## intra_te_cd_2  3 -43.087 -42.180 24.544  -49.087 0.0019      0     <2e-16 ***
## intra_te_cd_3  3 -43.086 -42.178 24.543  -49.086 0.0000      0          1    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(intra_te_cd_2)
##  Family: Gamma  ( log )
## Formula:          Te_intra + 1 ~ Environment
## Data: subset(param_all_w0, Tu_Regime == "SR1" & Te_Regime == "SR4")
## 
##      AIC      BIC   logLik deviance df.resid 
##    -43.1    -42.2     24.5    -49.1        7 
## 
## 
## Dispersion estimate for Gamma family (sigma^2): 0.000422 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)
## (Intercept)  0.005125   0.009189   0.558    0.577
## EnvironmentN 0.013499   0.012995   1.039    0.299
summary(intra_te_cd_1) #Again very similar estimates
##  Family: gaussian  ( identity )
## Formula:          Te_intra ~ Environment
## Data: subset(param_all_w0, Tu_Regime == "SR1" & Te_Regime == "SR4")
## 
##      AIC      BIC   logLik deviance df.resid 
##    -43.1    -42.2     24.5    -49.1        7 
## 
## 
## Dispersion estimate for gaussian family (sigma^2): 0.000432 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)
## (Intercept)  0.005138   0.009298   0.553    0.581
## EnvironmentN 0.013660   0.013150   1.039    0.299
simulationOutput <- simulateResiduals(fittedModel = intra_te_cd_1, plot = F)
plot(simulationOutput) #No problems
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.25. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.5. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.75. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.

######
inter_tu_cd_1<-glmmTMB(Tu_inter~Environment, data=subset(param_all_w0, (Tu_Regime=="SR1" & Te_Regime=="SR4")))
inter_tu_cd_2<-glmmTMB(Tu_inter+1~Environment, data=subset(param_all_w0, (Tu_Regime=="SR1" & Te_Regime=="SR4")), family=Gamma(link="log"))
inter_tu_cd_3<-glmmTMB(Tu_inter+1~Environment, data=subset(param_all_w0, (Tu_Regime=="SR1" & Te_Regime=="SR4")), family=gaussian(link="log"))
anova(inter_tu_cd_1,inter_tu_cd_2,inter_tu_cd_3)
## Data: subset(param_all_w0, (Tu_Regime == "SR1" & Te_Regime == "SR4"))
## Models:
## inter_tu_cd_1: Tu_inter ~ Environment, zi=~0, disp=~1
## inter_tu_cd_2: Tu_inter + 1 ~ Environment, zi=~0, disp=~1
## inter_tu_cd_3: Tu_inter + 1 ~ Environment, zi=~0, disp=~1
##               Df     AIC     BIC logLik deviance  Chisq Chi Df Pr(>Chisq)    
## inter_tu_cd_1  3 -44.339 -43.431 25.169  -50.339                             
## inter_tu_cd_2  3 -44.390 -43.483 25.195  -50.390 0.0518      0     <2e-16 ***
## inter_tu_cd_3  3 -44.339 -43.431 25.169  -50.339 0.0000      0          1    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(inter_tu_cd_2)
##  Family: Gamma  ( log )
## Formula:          Tu_inter + 1 ~ Environment
## Data: subset(param_all_w0, (Tu_Regime == "SR1" & Te_Regime == "SR4"))
## 
##      AIC      BIC   logLik deviance df.resid 
##    -44.4    -43.5     25.2    -50.4        7 
## 
## 
## Dispersion estimate for Gamma family (sigma^2): 0.000361 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)  
## (Intercept)  0.010748   0.008495   1.265   0.2058  
## EnvironmentN 0.028916   0.012014   2.407   0.0161 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(inter_tu_cd_1)
##  Family: gaussian  ( identity )
## Formula:          Tu_inter ~ Environment
## Data: subset(param_all_w0, (Tu_Regime == "SR1" & Te_Regime == "SR4"))
## 
##      AIC      BIC   logLik deviance df.resid 
##    -44.3    -43.4     25.2    -50.3        7 
## 
## 
## Dispersion estimate for gaussian family (sigma^2): 0.000381 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)  
## (Intercept)  0.010806   0.008734   1.237   0.2160  
## EnvironmentN 0.029655   0.012351   2.401   0.0163 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
simulationOutput <- simulateResiduals(fittedModel = inter_tu_cd_1, plot = F)
plot(simulationOutput) #no problems
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.25. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.5. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.75. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.

inter_te_cd_1<-glmmTMB(Te_inter~Environment, data=subset(param_all_w0, (Tu_Regime=="SR1" & Te_Regime=="SR4")))
inter_te_cd_2<-glmmTMB(Te_inter+1~Environment, data=subset(param_all_w0, (Tu_Regime=="SR1" & Te_Regime=="SR4")), family=Gamma(link="log"))
inter_te_cd_3<-glmmTMB(Te_inter+1~Environment, data=subset(param_all_w0, (Tu_Regime=="SR1" & Te_Regime=="SR4")), family=gaussian(link="log"))
anova(inter_te_cd_1,inter_te_cd_2,inter_te_cd_3)
## Data: subset(param_all_w0, (Tu_Regime == "SR1" & Te_Regime == "SR4"))
## Models:
## inter_te_cd_1: Te_inter ~ Environment, zi=~0, disp=~1
## inter_te_cd_2: Te_inter + 1 ~ Environment, zi=~0, disp=~1
## inter_te_cd_3: Te_inter + 1 ~ Environment, zi=~0, disp=~1
##               Df     AIC    BIC logLik deviance  Chisq Chi Df Pr(>Chisq)    
## inter_te_cd_1  3 -26.108 -25.20 16.054  -32.108                             
## inter_te_cd_2  3 -26.898 -25.99 16.449  -32.898 0.7904      0     <2e-16 ***
## inter_te_cd_3  3 -26.108 -25.20 16.054  -32.108 0.0000      0          1    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(inter_te_cd_2)
##  Family: Gamma  ( log )
## Formula:          Te_inter + 1 ~ Environment
## Data: subset(param_all_w0, (Tu_Regime == "SR1" & Te_Regime == "SR4"))
## 
##      AIC      BIC   logLik deviance df.resid 
##    -26.9    -26.0     16.4    -32.9        7 
## 
## 
## Dispersion estimate for Gamma family (sigma^2): 0.002 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  -0.01309    0.02000  -0.655    0.513    
## EnvironmentN  0.11493    0.02828   4.064 4.82e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(inter_te_cd_1)
##  Family: gaussian  ( identity )
## Formula:          Te_inter ~ Environment
## Data: subset(param_all_w0, (Tu_Regime == "SR1" & Te_Regime == "SR4"))
## 
##      AIC      BIC   logLik deviance df.resid 
##    -26.1    -25.2     16.1    -32.1        7 
## 
## 
## Dispersion estimate for gaussian family (sigma^2): 0.00236 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  -0.01300    0.02173  -0.598     0.55    
## EnvironmentN  0.12021    0.03073   3.912 9.17e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
simulationOutput <- simulateResiduals(fittedModel = inter_te_cd_1, plot = F)
plot(simulationOutput) #No problems
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.25. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.5. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.75. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.

Summary
summary(gr_tu_cd_2)
##  Family: Gamma  ( log )
## Formula:          Tu_lambda ~ Environment
## Data: subset(param_all_w0, Tu_Regime == "SR1" & Te_Regime == "SR4")
## 
##      AIC      BIC   logLik deviance df.resid 
##      5.3      6.2      0.3     -0.7        7 
## 
## 
## Dispersion estimate for Gamma family (sigma^2): 0.0181 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)    0.2006     0.0601   3.338 0.000844 ***
## EnvironmentN   0.7211     0.0850   8.484  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(gr_te_cd_2)
##  Family: Gamma  ( log )
## Formula:          Te_lambda ~ Environment
## Data: subset(param_all_w0, Tu_Regime == "SR1" & Te_Regime == "SR4")
## 
##      AIC      BIC   logLik deviance df.resid 
##     22.1     23.0     -8.1     16.1        7 
## 
## 
## Dispersion estimate for Gamma family (sigma^2): 0.0298 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)   0.56092    0.07726    7.26 3.87e-13 ***
## EnvironmentN  1.18262    0.10926   10.82  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(intra_tu_cd_1) 
##  Family: gaussian  ( identity )
## Formula:          Tu_intra ~ Environment
## Data: subset(param_all_w0, Tu_Regime == "SR1" & Te_Regime == "SR4")
## 
##      AIC      BIC   logLik deviance df.resid 
##    -40.1    -39.1     23.0    -46.1        7 
## 
## 
## Dispersion estimate for gaussian family (sigma^2): 0.000586 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)
## (Intercept)  0.009066   0.010821   0.838    0.402
## EnvironmentN 0.019251   0.015304   1.258    0.208
summary(intra_te_cd_1)
##  Family: gaussian  ( identity )
## Formula:          Te_intra ~ Environment
## Data: subset(param_all_w0, Tu_Regime == "SR1" & Te_Regime == "SR4")
## 
##      AIC      BIC   logLik deviance df.resid 
##    -43.1    -42.2     24.5    -49.1        7 
## 
## 
## Dispersion estimate for gaussian family (sigma^2): 0.000432 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)
## (Intercept)  0.005138   0.009298   0.553    0.581
## EnvironmentN 0.013660   0.013150   1.039    0.299
summary(inter_tu_cd_1)
##  Family: gaussian  ( identity )
## Formula:          Tu_inter ~ Environment
## Data: subset(param_all_w0, (Tu_Regime == "SR1" & Te_Regime == "SR4"))
## 
##      AIC      BIC   logLik deviance df.resid 
##    -44.3    -43.4     25.2    -50.3        7 
## 
## 
## Dispersion estimate for gaussian family (sigma^2): 0.000381 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)  
## (Intercept)  0.010806   0.008734   1.237   0.2160  
## EnvironmentN 0.029655   0.012351   2.401   0.0163 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(inter_te_cd_1)
##  Family: gaussian  ( identity )
## Formula:          Te_inter ~ Environment
## Data: subset(param_all_w0, (Tu_Regime == "SR1" & Te_Regime == "SR4"))
## 
##      AIC      BIC   logLik deviance df.resid 
##    -26.1    -25.2     16.1    -32.1        7 
## 
## 
## Dispersion estimate for gaussian family (sigma^2): 0.00236 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  -0.01300    0.02173  -0.598     0.55    
## EnvironmentN  0.12021    0.03073   3.912 9.17e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Anova(gr_tu_cd_2)
## Analysis of Deviance Table (Type II Wald chisquare tests)
## 
## Response: Tu_lambda
##              Chisq Df Pr(>Chisq)    
## Environment 71.985  1  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Anova(gr_te_cd_2)
## Analysis of Deviance Table (Type II Wald chisquare tests)
## 
## Response: Te_lambda
##              Chisq Df Pr(>Chisq)    
## Environment 117.15  1  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Anova(intra_tu_cd_1) 
## Analysis of Deviance Table (Type II Wald chisquare tests)
## 
## Response: Tu_intra
##              Chisq Df Pr(>Chisq)
## Environment 1.5823  1     0.2084
Anova(intra_te_cd_1)
## Analysis of Deviance Table (Type II Wald chisquare tests)
## 
## Response: Te_intra
##              Chisq Df Pr(>Chisq)
## Environment 1.0791  1     0.2989
Anova(inter_tu_cd_1)
## Analysis of Deviance Table (Type II Wald chisquare tests)
## 
## Response: Tu_inter
##              Chisq Df Pr(>Chisq)  
## Environment 5.7649  1    0.01635 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Anova(inter_te_cd_1)
## Analysis of Deviance Table (Type II Wald chisquare tests)
## 
## Response: Te_inter
##             Chisq Df Pr(>Chisq)    
## Environment  15.3  1   9.17e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

2.3.3 - Does evolution change the performance?

gr_tu_ev_1<-glmmTMB(Tu_lambda~Tu_Regime, data=subset(param_all_w0, Environment=="Cd" & Te_Regime=="SR4"))
gr_tu_ev_2<-glmmTMB(Tu_lambda~Tu_Regime, data=subset(param_all_w0, Environment=="Cd"& Te_Regime=="SR4"), family=Gamma(link="log"))
gr_tu_ev_3<-glmmTMB(Tu_lambda~Tu_Regime, data=subset(param_all_w0, Environment=="Cd"& Te_Regime=="SR4"), family=gaussian(link="log"))
anova(gr_tu_ev_1,gr_tu_ev_2,gr_tu_ev_3)
## Data: subset(param_all_w0, Environment == "Cd" & Te_Regime == "SR4")
## Models:
## gr_tu_ev_1: Tu_lambda ~ Tu_Regime, zi=~0, disp=~1
## gr_tu_ev_2: Tu_lambda ~ Tu_Regime, zi=~0, disp=~1
## gr_tu_ev_3: Tu_lambda ~ Tu_Regime, zi=~0, disp=~1
##            Df     AIC     BIC logLik deviance  Chisq Chi Df Pr(>Chisq)    
## gr_tu_ev_1  3 -7.6268 -7.0351 6.8134  -13.627                             
## gr_tu_ev_2  3 -7.8489 -7.2572 6.9244  -13.849 0.2221      0     <2e-16 ***
## gr_tu_ev_3  3 -7.6268 -7.0351 6.8134  -13.627 0.0000      0          1    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(gr_tu_ev_2)
##  Family: Gamma  ( log )
## Formula:          Tu_lambda ~ Tu_Regime
## Data: subset(param_all_w0, Environment == "Cd" & Te_Regime == "SR4")
## 
##      AIC      BIC   logLik deviance df.resid 
##     -7.8     -7.3      6.9    -13.8        6 
## 
## 
## Dispersion estimate for Gamma family (sigma^2): 0.00744 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)   0.20062    0.03858   5.201 1.98e-07 ***
## Tu_RegimeSR2  0.14393    0.05786   2.487   0.0129 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(gr_tu_ev_1)
##  Family: gaussian  ( identity )
## Formula:          Tu_lambda ~ Tu_Regime
## Data: subset(param_all_w0, Environment == "Cd" & Te_Regime == "SR4")
## 
##      AIC      BIC   logLik deviance df.resid 
##     -7.6     -7.0      6.8    -13.6        6 
## 
## 
## Dispersion estimate for gaussian family (sigma^2): 0.0129 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)   1.22216    0.05076  24.079   <2e-16 ***
## Tu_RegimeSR2  0.18919    0.07614   2.485    0.013 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
simulationOutput <- simulateResiduals(fittedModel = gr_tu_ev_2, plot = F)
plot(simulationOutput) #no problems
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.25. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.5. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.75. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.

gr_te_ev_1<-glmmTMB(Te_lambda~Te_Regime, data=subset(param_all_w0, Environment=="Cd"& Tu_Regime=="SR1"))
gr_te_ev_2<-glmmTMB(Te_lambda~Te_Regime, data=subset(param_all_w0, Environment=="Cd"& Tu_Regime=="SR1"), family=Gamma(link="log"))
gr_te_ev_3<-glmmTMB(Te_lambda~Te_Regime, data=subset(param_all_w0, Environment=="Cd"& Tu_Regime=="SR1"), family=gaussian(link="log"))
anova(gr_te_ev_1,gr_te_ev_2,gr_te_ev_3)
## Data: subset(param_all_w0, Environment == "Cd" & Tu_Regime == "SR1")
## Models:
## gr_te_ev_1: Te_lambda ~ Te_Regime, zi=~0, disp=~1
## gr_te_ev_2: Te_lambda ~ Te_Regime, zi=~0, disp=~1
## gr_te_ev_3: Te_lambda ~ Te_Regime, zi=~0, disp=~1
##            Df    AIC    BIC  logLik deviance  Chisq Chi Df Pr(>Chisq)    
## gr_te_ev_1  3 12.699 13.607 -3.3494   6.6989                             
## gr_te_ev_2  3 12.238 13.146 -3.1192   6.2384 0.4605      0     <2e-16 ***
## gr_te_ev_3  3 12.699 13.607 -3.3494   6.6989 0.0000      0          1    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(gr_te_ev_2)
##  Family: Gamma  ( log )
## Formula:          Te_lambda ~ Te_Regime
## Data: subset(param_all_w0, Environment == "Cd" & Tu_Regime == "SR1")
## 
##      AIC      BIC   logLik deviance df.resid 
##     12.2     13.1     -3.1      6.2        7 
## 
## 
## Dispersion estimate for Gamma family (sigma^2): 0.0289 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)   0.56092    0.07602   7.379  1.6e-13 ***
## Te_RegimeSR5  0.22763    0.10751   2.117   0.0342 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(gr_te_ev_1)
##  Family: gaussian  ( identity )
## Formula:          Te_lambda ~ Te_Regime
## Data: subset(param_all_w0, Environment == "Cd" & Tu_Regime == "SR1")
## 
##      AIC      BIC   logLik deviance df.resid 
##     12.7     13.6     -3.3      6.7        7 
## 
## 
## Dispersion estimate for gaussian family (sigma^2): 0.114 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)    1.7523     0.1513  11.584   <2e-16 ***
## Te_RegimeSR5   0.4479     0.2139   2.094   0.0363 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
simulationOutput <- simulateResiduals(fittedModel = gr_te_ev_2, plot = F)
plot(simulationOutput)# No problems
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.25. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.5. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.75. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.

## intra

intra_tu_ev_1<-glmmTMB(Tu_intra~Tu_Regime, data=subset(param_all_w0, Environment=="Cd"& Te_Regime=="SR4"))
intra_tu_ev_2<-glmmTMB(Tu_intra+1~Tu_Regime, data=subset(param_all_w0, Environment=="Cd"& Te_Regime=="SR4"), family=Gamma(link="log"))
intra_tu_ev_3<-glmmTMB(Tu_intra+1~Tu_Regime, data=subset(param_all_w0, Environment=="Cd"& Te_Regime=="SR4"), family=gaussian(link="log"))
anova(intra_tu_ev_1,intra_tu_ev_2,intra_tu_ev_3)
## Data: subset(param_all_w0, Environment == "Cd" & Te_Regime == "SR4")
## Models:
## intra_tu_ev_1: Tu_intra ~ Tu_Regime, zi=~0, disp=~1
## intra_tu_ev_2: Tu_intra + 1 ~ Tu_Regime, zi=~0, disp=~1
## intra_tu_ev_3: Tu_intra + 1 ~ Tu_Regime, zi=~0, disp=~1
##               Df     AIC     BIC logLik deviance  Chisq Chi Df Pr(>Chisq)    
## intra_tu_ev_1  3 -43.401 -42.809 24.700  -49.401                             
## intra_tu_ev_2  3 -43.426 -42.835 24.713  -49.426 0.0259      0     <2e-16 ***
## intra_tu_ev_3  3 -43.401 -42.809 24.700  -49.401 0.0000      0          1    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(intra_tu_ev_2)
##  Family: Gamma  ( log )
## Formula:          Tu_intra + 1 ~ Tu_Regime
## Data: subset(param_all_w0, Environment == "Cd" & Te_Regime == "SR4")
## 
##      AIC      BIC   logLik deviance df.resid 
##    -43.4    -42.8     24.7    -49.4        6 
## 
## 
## Dispersion estimate for Gamma family (sigma^2): 0.000236 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)
## (Intercept)  0.009025   0.006873   1.313    0.189
## Tu_RegimeSR2 0.003735   0.010309   0.362    0.717
summary(intra_tu_ev_1)
##  Family: gaussian  ( identity )
## Formula:          Tu_intra ~ Tu_Regime
## Data: subset(param_all_w0, Environment == "Cd" & Te_Regime == "SR4")
## 
##      AIC      BIC   logLik deviance df.resid 
##    -43.4    -42.8     24.7    -49.4        6 
## 
## 
## Dispersion estimate for gaussian family (sigma^2): 0.000242 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)
## (Intercept)  0.009066   0.006956   1.303    0.192
## Tu_RegimeSR2 0.003776   0.010434   0.362    0.717
simulationOutput <- simulateResiduals(fittedModel = intra_tu_ev_1, plot = F)
plot(simulationOutput) #no problems
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.25. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.5. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.75. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.

intra_te_ev_1<-glmmTMB(Te_intra~Te_Regime, data=subset(param_all_w0, Environment=="Cd"& Tu_Regime=="SR1"))
intra_te_ev_2<-glmmTMB(Te_intra+1~Te_Regime, data=subset(param_all_w0, Environment=="Cd"& Tu_Regime=="SR1"), family=Gamma(link="log"))
intra_te_ev_3<-glmmTMB(Te_intra+1~Te_Regime, data=subset(param_all_w0, Environment=="Cd"& Tu_Regime=="SR1"), family=gaussian(link="log"))
anova(intra_te_ev_1,intra_te_ev_2,intra_te_ev_3)
## Data: subset(param_all_w0, Environment == "Cd" & Tu_Regime == "SR1")
## Models:
## intra_te_ev_1: Te_intra ~ Te_Regime, zi=~0, disp=~1
## intra_te_ev_2: Te_intra + 1 ~ Te_Regime, zi=~0, disp=~1
## intra_te_ev_3: Te_intra + 1 ~ Te_Regime, zi=~0, disp=~1
##               Df     AIC     BIC logLik deviance  Chisq Chi Df Pr(>Chisq)    
## intra_te_ev_1  3 -49.045 -48.137 27.522  -55.045                             
## intra_te_ev_2  3 -49.035 -48.127 27.518  -55.035 0.0000      0          1    
## intra_te_ev_3  3 -49.045 -48.137 27.522  -55.045 0.0094      0     <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(intra_te_ev_3)
##  Family: gaussian  ( log )
## Formula:          Te_intra + 1 ~ Te_Regime
## Data: subset(param_all_w0, Environment == "Cd" & Tu_Regime == "SR1")
## 
##      AIC      BIC   logLik deviance df.resid 
##    -49.0    -48.1     27.5    -55.0        7 
## 
## 
## Dispersion estimate for gaussian family (sigma^2): 0.000238 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)   
## (Intercept)  0.005125   0.006867   0.746  0.45546   
## Te_RegimeSR5 0.028033   0.009578   2.927  0.00342 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(intra_te_ev_1)
##  Family: gaussian  ( identity )
## Formula:          Te_intra ~ Te_Regime
## Data: subset(param_all_w0, Environment == "Cd" & Tu_Regime == "SR1")
## 
##      AIC      BIC   logLik deviance df.resid 
##    -49.0    -48.1     27.5    -55.0        7 
## 
## 
## Dispersion estimate for gaussian family (sigma^2): 0.000238 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)   
## (Intercept)  0.005138   0.006902   0.744  0.45661   
## Te_RegimeSR5 0.028576   0.009761   2.928  0.00342 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
simulationOutput <- simulateResiduals(fittedModel = intra_te_ev_1, plot = F)
plot(simulationOutput) #no problems
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.25. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.5. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.75. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.

## inter

inter_tu_ev_1<-glmmTMB(Tu_inter~Tu_Regime*Te_Regime, data=subset(param_all_w0, Environment=="Cd"))
inter_tu_ev_2<-glmmTMB(Tu_inter+1~Tu_Regime*Te_Regime, data=subset(param_all_w0, Environment=="Cd"), family=Gamma(link="log"))
inter_tu_ev_3<-glmmTMB(Tu_inter+1~Tu_Regime*Te_Regime, data=subset(param_all_w0, Environment=="Cd"), family=gaussian(link="log"))
anova(inter_tu_ev_1,inter_tu_ev_2,inter_tu_ev_3)
## Data: subset(param_all_w0, Environment == "Cd")
## Models:
## inter_tu_ev_1: Tu_inter ~ Tu_Regime * Te_Regime, zi=~0, disp=~1
## inter_tu_ev_2: Tu_inter + 1 ~ Tu_Regime * Te_Regime, zi=~0, disp=~1
## inter_tu_ev_3: Tu_inter + 1 ~ Tu_Regime * Te_Regime, zi=~0, disp=~1
##               Df     AIC     BIC logLik deviance  Chisq Chi Df Pr(>Chisq)    
## inter_tu_ev_1  5 -87.807 -83.355 48.903  -97.807                             
## inter_tu_ev_2  5 -87.725 -83.273 48.863  -97.725 0.0000      0          1    
## inter_tu_ev_3  5 -87.807 -83.355 48.903  -97.807 0.0819      0     <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(inter_tu_ev_3)
##  Family: gaussian  ( log )
## Formula:          Tu_inter + 1 ~ Tu_Regime * Te_Regime
## Data: subset(param_all_w0, Environment == "Cd")
## 
##      AIC      BIC   logLik deviance df.resid 
##    -87.8    -83.4     48.9    -97.8       13 
## 
## 
## Dispersion estimate for gaussian family (sigma^2): 0.000256 
## 
## Conditional model:
##                            Estimate Std. Error z value Pr(>|z|)
## (Intercept)                0.010748   0.007074   1.519    0.129
## Tu_RegimeSR2               0.003855   0.010589   0.364    0.716
## Te_RegimeSR5              -0.011809   0.010064  -1.173    0.241
## Tu_RegimeSR2:Te_RegimeSR5  0.005246   0.015042   0.349    0.727
summary(inter_tu_ev_1)
##  Family: gaussian  ( identity )
## Formula:          Tu_inter ~ Tu_Regime * Te_Regime
## Data: subset(param_all_w0, Environment == "Cd")
## 
##      AIC      BIC   logLik deviance df.resid 
##    -87.8    -83.4     48.9    -97.8       13 
## 
## 
## Dispersion estimate for gaussian family (sigma^2): 0.000256 
## 
## Conditional model:
##                            Estimate Std. Error z value Pr(>|z|)
## (Intercept)                0.010806   0.007151   1.511    0.131
## Tu_RegimeSR2               0.003905   0.010726   0.364    0.716
## Te_RegimeSR5              -0.011866   0.010113  -1.173    0.241
## Tu_RegimeSR2:Te_RegimeSR5  0.005228   0.015169   0.345    0.730
simulationOutput <- simulateResiduals(fittedModel = inter_tu_ev_1, plot = F)
plot(simulationOutput) #no problem

pairs(emmeans(inter_tu_ev_1, pairwise~Te_Regime:Tu_Regime), adjust="none")
##  contrast          estimate     SE df t.ratio p.value
##  SR4 SR1 - SR5 SR1  0.01187 0.0101 13   1.173  0.2617
##  SR4 SR1 - SR4 SR2 -0.00390 0.0107 13  -0.364  0.7217
##  SR4 SR1 - SR5 SR2  0.00273 0.0107 13   0.255  0.8029
##  SR5 SR1 - SR4 SR2 -0.01577 0.0107 13  -1.470  0.1653
##  SR5 SR1 - SR5 SR2 -0.00913 0.0107 13  -0.851  0.4099
##  SR4 SR2 - SR5 SR2  0.00664 0.0113 13   0.587  0.5672
inter_te_ev_1<-glmmTMB(Te_inter~Te_Regime*Tu_Regime, data=subset(param_all_w0, Environment=="Cd"))
inter_te_ev_2<-glmmTMB(Te_inter+1~Te_Regime*Tu_Regime, data=subset(param_all_w0, Environment=="Cd"), family=Gamma(link="log"))
inter_te_ev_3<-glmmTMB(Te_inter+1~Te_Regime*Tu_Regime, data=subset(param_all_w0, Environment=="Cd"), family=gaussian(link="log"))
anova(inter_te_ev_1,inter_te_ev_2,inter_te_ev_3)
## Data: subset(param_all_w0, Environment == "Cd")
## Models:
## inter_te_ev_1: Te_inter ~ Te_Regime * Tu_Regime, zi=~0, disp=~1
## inter_te_ev_2: Te_inter + 1 ~ Te_Regime * Tu_Regime, zi=~0, disp=~1
## inter_te_ev_3: Te_inter + 1 ~ Te_Regime * Tu_Regime, zi=~0, disp=~1
##               Df     AIC     BIC logLik deviance Chisq Chi Df Pr(>Chisq)    
## inter_te_ev_1  5 -74.432 -69.980 42.216  -84.432                            
## inter_te_ev_2  5 -74.123 -69.671 42.061  -84.123 0.000      0          1    
## inter_te_ev_3  5 -74.432 -69.980 42.216  -84.432 0.309      0     <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(inter_te_ev_3)
##  Family: gaussian  ( log )
## Formula:          Te_inter + 1 ~ Te_Regime * Tu_Regime
## Data: subset(param_all_w0, Environment == "Cd")
## 
##      AIC      BIC   logLik deviance df.resid 
##    -74.4    -70.0     42.2    -84.4       13 
## 
## 
## Dispersion estimate for gaussian family (sigma^2): 0.000538 
## 
## Conditional model:
##                           Estimate Std. Error z value Pr(>|z|)    
## (Intercept)               -0.01309    0.01051  -1.246   0.2127    
## Te_RegimeSR5               0.05236    0.01448   3.616   0.0003 ***
## Tu_RegimeSR2               0.01487    0.01563   0.951   0.3415    
## Te_RegimeSR5:Tu_RegimeSR2 -0.05149    0.02185  -2.357   0.0184 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(inter_te_ev_1)
##  Family: gaussian  ( identity )
## Formula:          Te_inter ~ Te_Regime * Tu_Regime
## Data: subset(param_all_w0, Environment == "Cd")
## 
##      AIC      BIC   logLik deviance df.resid 
##    -74.4    -70.0     42.2    -84.4       13 
## 
## 
## Dispersion estimate for gaussian family (sigma^2): 0.000538 
## 
## Conditional model:
##                           Estimate Std. Error z value Pr(>|z|)    
## (Intercept)               -0.01300    0.01037  -1.254 0.209753    
## Te_RegimeSR5               0.05306    0.01466   3.618 0.000296 ***
## Tu_RegimeSR2               0.01478    0.01555   0.951 0.341857    
## Te_RegimeSR5:Tu_RegimeSR2 -0.05218    0.02199  -2.372 0.017672 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
pairs(emmeans(inter_te_ev_1, pairwise~Te_Regime:Tu_Regime), adjust="none")
##  contrast           estimate     SE df t.ratio p.value
##  SR4 SR1 - SR5 SR1 -0.053059 0.0147 13  -3.618  0.0031
##  SR4 SR1 - SR4 SR2 -0.014783 0.0156 13  -0.951  0.3592
##  SR4 SR1 - SR5 SR2 -0.015661 0.0156 13  -1.007  0.3323
##  SR5 SR1 - SR4 SR2  0.038276 0.0156 13   2.461  0.0286
##  SR5 SR1 - SR5 SR2  0.037398 0.0156 13   2.405  0.0318
##  SR4 SR2 - SR5 SR2 -0.000878 0.0164 13  -0.054  0.9581
simulationOutput <- simulateResiduals(fittedModel = inter_te_ev_1, plot = F, )
#plot(simulationOutput)
plotResiduals(simulationOutput, subset(param_all_w0, Environment=="Cd")$Te_Regime)
## Warning in ensurePredictor(simulationOutput, form): DHARMa:::ensurePredictor:
## character string was provided as predictor. DHARMa has converted to factor
## automatically. To remove this warning, please convert to factor before
## attempting to plot with DHARMa.

plotResiduals(simulationOutput, subset(param_all_w0, Environment=="Cd")$Tu_Regime)
## Warning in ensurePredictor(simulationOutput, form): DHARMa:::ensurePredictor:
## character string was provided as predictor. DHARMa has converted to factor
## automatically. To remove this warning, please convert to factor before
## attempting to plot with DHARMa.

# No problem
Summary
summary(gr_tu_ev_2)
##  Family: Gamma  ( log )
## Formula:          Tu_lambda ~ Tu_Regime
## Data: subset(param_all_w0, Environment == "Cd" & Te_Regime == "SR4")
## 
##      AIC      BIC   logLik deviance df.resid 
##     -7.8     -7.3      6.9    -13.8        6 
## 
## 
## Dispersion estimate for Gamma family (sigma^2): 0.00744 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)   0.20062    0.03858   5.201 1.98e-07 ***
## Tu_RegimeSR2  0.14393    0.05786   2.487   0.0129 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(gr_te_ev_2)
##  Family: Gamma  ( log )
## Formula:          Te_lambda ~ Te_Regime
## Data: subset(param_all_w0, Environment == "Cd" & Tu_Regime == "SR1")
## 
##      AIC      BIC   logLik deviance df.resid 
##     12.2     13.1     -3.1      6.2        7 
## 
## 
## Dispersion estimate for Gamma family (sigma^2): 0.0289 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)   0.56092    0.07602   7.379  1.6e-13 ***
## Te_RegimeSR5  0.22763    0.10751   2.117   0.0342 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## intra

summary(intra_tu_ev_1)
##  Family: gaussian  ( identity )
## Formula:          Tu_intra ~ Tu_Regime
## Data: subset(param_all_w0, Environment == "Cd" & Te_Regime == "SR4")
## 
##      AIC      BIC   logLik deviance df.resid 
##    -43.4    -42.8     24.7    -49.4        6 
## 
## 
## Dispersion estimate for gaussian family (sigma^2): 0.000242 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)
## (Intercept)  0.009066   0.006956   1.303    0.192
## Tu_RegimeSR2 0.003776   0.010434   0.362    0.717
summary(intra_te_ev_1)
##  Family: gaussian  ( identity )
## Formula:          Te_intra ~ Te_Regime
## Data: subset(param_all_w0, Environment == "Cd" & Tu_Regime == "SR1")
## 
##      AIC      BIC   logLik deviance df.resid 
##    -49.0    -48.1     27.5    -55.0        7 
## 
## 
## Dispersion estimate for gaussian family (sigma^2): 0.000238 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)   
## (Intercept)  0.005138   0.006902   0.744  0.45661   
## Te_RegimeSR5 0.028576   0.009761   2.928  0.00342 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## inter

pairs(emmeans(inter_tu_ev_1, pairwise~Te_Regime:Tu_Regime), adjust="none")
##  contrast          estimate     SE df t.ratio p.value
##  SR4 SR1 - SR5 SR1  0.01187 0.0101 13   1.173  0.2617
##  SR4 SR1 - SR4 SR2 -0.00390 0.0107 13  -0.364  0.7217
##  SR4 SR1 - SR5 SR2  0.00273 0.0107 13   0.255  0.8029
##  SR5 SR1 - SR4 SR2 -0.01577 0.0107 13  -1.470  0.1653
##  SR5 SR1 - SR5 SR2 -0.00913 0.0107 13  -0.851  0.4099
##  SR4 SR2 - SR5 SR2  0.00664 0.0113 13   0.587  0.5672
pairs(emmeans(inter_te_ev_1, pairwise~Te_Regime:Tu_Regime), adjust="none")
##  contrast           estimate     SE df t.ratio p.value
##  SR4 SR1 - SR5 SR1 -0.053059 0.0147 13  -3.618  0.0031
##  SR4 SR1 - SR4 SR2 -0.014783 0.0156 13  -0.951  0.3592
##  SR4 SR1 - SR5 SR2 -0.015661 0.0156 13  -1.007  0.3323
##  SR5 SR1 - SR4 SR2  0.038276 0.0156 13   2.461  0.0286
##  SR5 SR1 - SR5 SR2  0.037398 0.0156 13   2.405  0.0318
##  SR4 SR2 - SR5 SR2 -0.000878 0.0164 13  -0.054  0.9581
# Anova

Anova(gr_tu_ev_2)
## Analysis of Deviance Table (Type II Wald chisquare tests)
## 
## Response: Tu_lambda
##            Chisq Df Pr(>Chisq)  
## Tu_Regime 6.1871  1    0.01287 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Anova(gr_te_ev_2)
## Analysis of Deviance Table (Type II Wald chisquare tests)
## 
## Response: Te_lambda
##            Chisq Df Pr(>Chisq)  
## Te_Regime 4.4834  1    0.03423 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## intra

Anova(intra_tu_ev_1)
## Analysis of Deviance Table (Type II Wald chisquare tests)
## 
## Response: Tu_intra
##           Chisq Df Pr(>Chisq)
## Tu_Regime 0.131  1     0.7174
Anova(intra_te_ev_1)
## Analysis of Deviance Table (Type II Wald chisquare tests)
## 
## Response: Te_intra
##           Chisq Df Pr(>Chisq)   
## Te_Regime  8.57  1   0.003418 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Inter
Anova(inter_tu_ev_1, type=3)
## Analysis of Deviance Table (Type III Wald chisquare tests)
## 
## Response: Tu_inter
##                      Chisq Df Pr(>Chisq)
## (Intercept)         2.2835  1     0.1308
## Tu_Regime           0.1325  1     0.7158
## Te_Regime           1.3767  1     0.2407
## Tu_Regime:Te_Regime 0.1188  1     0.7304
Anova(inter_te_ev_1, type=3)
## Analysis of Deviance Table (Type III Wald chisquare tests)
## 
## Response: Te_inter
##                       Chisq Df Pr(>Chisq)    
## (Intercept)          1.5731  1  0.2097531    
## Te_Regime           13.0935  1  0.0002963 ***
## Tu_Regime            0.9035  1  0.3418567    
## Te_Regime:Tu_Regime  5.6283  1  0.0176724 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

2.3.4 - Does evolution change the ancestral?

gr_tu_an_1<-glmmTMB(Tu_lambda~Tu_Regime, data=subset(param_all_w0, Environment=="N" & Te_Regime=="SR4"))
gr_tu_an_2<-glmmTMB(Tu_lambda~Tu_Regime, data=subset(param_all_w0, Environment=="N"& Te_Regime=="SR4"), family=Gamma(link="log"))
gr_tu_an_3<-glmmTMB(Tu_lambda~Tu_Regime, data=subset(param_all_w0, Environment=="N"& Te_Regime=="SR4"), family=gaussian(link="log"))
anova(gr_tu_an_1,gr_tu_an_2,gr_tu_an_3)
## Data: subset(param_all_w0, Environment == "N" & Te_Regime == "SR4")
## Models:
## gr_tu_an_1: Tu_lambda ~ Tu_Regime, zi=~0, disp=~1
## gr_tu_an_2: Tu_lambda ~ Tu_Regime, zi=~0, disp=~1
## gr_tu_an_3: Tu_lambda ~ Tu_Regime, zi=~0, disp=~1
##            Df    AIC    BIC  logLik deviance  Chisq Chi Df Pr(>Chisq)    
## gr_tu_an_1  3 19.212 19.803 -6.6058   13.212                             
## gr_tu_an_2  3 18.643 19.235 -6.3215   12.643 0.5685      0     <2e-16 ***
## gr_tu_an_3  3 19.212 19.803 -6.6058   13.212 0.0000      0          1    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(gr_tu_an_2)
##  Family: Gamma  ( log )
## Formula:          Tu_lambda ~ Tu_Regime
## Data: subset(param_all_w0, Environment == "N" & Te_Regime == "SR4")
## 
##      AIC      BIC   logLik deviance df.resid 
##     18.6     19.2     -6.3     12.6        6 
## 
## 
## Dispersion estimate for Gamma family (sigma^2): 0.0372 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)   0.92178    0.08625  10.688   <2e-16 ***
## Tu_RegimeSR2  0.04502    0.12937   0.348    0.728    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(gr_tu_an_1)
##  Family: gaussian  ( identity )
## Formula:          Tu_lambda ~ Tu_Regime
## Data: subset(param_all_w0, Environment == "N" & Te_Regime == "SR4")
## 
##      AIC      BIC   logLik deviance df.resid 
##     19.2     19.8     -6.6     13.2        6 
## 
## 
## Dispersion estimate for gaussian family (sigma^2): 0.254 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)    2.5138     0.2254  11.150   <2e-16 ***
## Tu_RegimeSR2   0.1158     0.3382   0.342    0.732    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
simulationOutput <- simulateResiduals(fittedModel = gr_tu_an_2, plot = F, )
plot(simulationOutput)# no problem
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.25. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.5. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.75. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.

gr_te_an_1<-glmmTMB(Te_lambda~Te_Regime, data=subset(param_all_w0, Environment=="N"& Tu_Regime=="SR1"))
gr_te_an_2<-glmmTMB(Te_lambda~Te_Regime, data=subset(param_all_w0, Environment=="N"& Tu_Regime=="SR1"), family=Gamma(link="log"))
gr_te_an_3<-glmmTMB(Te_lambda~Te_Regime, data=subset(param_all_w0, Environment=="N"& Tu_Regime=="SR1"), family=gaussian(link="log"))
anova(gr_te_an_1,gr_te_an_2,gr_te_an_3)
## Data: subset(param_all_w0, Environment == "N" & Tu_Regime == "SR1")
## Models:
## gr_te_an_1: Te_lambda ~ Te_Regime, zi=~0, disp=~1
## gr_te_an_2: Te_lambda ~ Te_Regime, zi=~0, disp=~1
## gr_te_an_3: Te_lambda ~ Te_Regime, zi=~0, disp=~1
##            Df    AIC    BIC  logLik deviance  Chisq Chi Df Pr(>Chisq)    
## gr_te_an_1  3 33.492 34.399 -13.746   27.491                             
## gr_te_an_2  3 31.700 32.608 -12.850   25.700 1.7918      0     <2e-16 ***
## gr_te_an_3  3 33.492 34.399 -13.746   27.491 0.0000      0          1    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(gr_te_an_2)
##  Family: Gamma  ( log )
## Formula:          Te_lambda ~ Te_Regime
## Data: subset(param_all_w0, Environment == "N" & Tu_Regime == "SR1")
## 
##      AIC      BIC   logLik deviance df.resid 
##     31.7     32.6    -12.8     25.7        7 
## 
## 
## Dispersion estimate for Gamma family (sigma^2): 0.0283 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)   1.74354    0.07529  23.157   <2e-16 ***
## Te_RegimeSR5 -0.17262    0.10648  -1.621    0.105    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
simulationOutput <- simulateResiduals(fittedModel = gr_te_an_2, plot = F, )
plot(simulationOutput)
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.25. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.5. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.75. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.

## intra

intra_tu_an_1<-glmmTMB(Tu_intra~Tu_Regime, data=subset(param_all_w0, Environment=="N"& Te_Regime=="SR4"))
intra_tu_an_2<-glmmTMB(Tu_intra+1~Tu_Regime, data=subset(param_all_w0, Environment=="N"& Te_Regime=="SR4"), family=Gamma(link="log"))
intra_tu_an_3<-glmmTMB(Tu_intra+1~Tu_Regime, data=subset(param_all_w0, Environment=="N"& Te_Regime=="SR4"), family=gaussian(link="log"))
anova(intra_tu_an_1,intra_tu_an_2,intra_tu_an_3)
## Data: subset(param_all_w0, Environment == "N" & Te_Regime == "SR4")
## Models:
## intra_tu_an_1: Tu_intra ~ Tu_Regime, zi=~0, disp=~1
## intra_tu_an_2: Tu_intra + 1 ~ Tu_Regime, zi=~0, disp=~1
## intra_tu_an_3: Tu_intra + 1 ~ Tu_Regime, zi=~0, disp=~1
##               Df     AIC     BIC logLik deviance  Chisq Chi Df Pr(>Chisq)    
## intra_tu_an_1  3 -30.949 -30.357 18.474  -36.949                             
## intra_tu_an_2  3 -30.931 -30.339 18.465  -36.931 0.0000      0          1    
## intra_tu_an_3  3 -30.949 -30.357 18.474  -36.949 0.0184      0     <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(intra_tu_an_3)
##  Family: gaussian  ( log )
## Formula:          Tu_intra + 1 ~ Tu_Regime
## Data: subset(param_all_w0, Environment == "N" & Te_Regime == "SR4")
## 
##      AIC      BIC   logLik deviance df.resid 
##    -30.9    -30.4     18.5    -36.9        6 
## 
## 
## Dispersion estimate for gaussian family (sigma^2): 0.000965 
## 
## Conditional model:
##                Estimate Std. Error z value Pr(>|z|)  
## (Intercept)   2.792e-02  1.351e-02   2.067   0.0388 *
## Tu_RegimeSR2 -6.347e-05  2.027e-02  -0.003   0.9975  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(intra_tu_an_1)
##  Family: gaussian  ( identity )
## Formula:          Tu_intra ~ Tu_Regime
## Data: subset(param_all_w0, Environment == "N" & Te_Regime == "SR4")
## 
##      AIC      BIC   logLik deviance df.resid 
##    -30.9    -30.4     18.5    -36.9        6 
## 
## 
## Dispersion estimate for gaussian family (sigma^2): 0.000965 
## 
## Conditional model:
##                Estimate Std. Error z value Pr(>|z|)  
## (Intercept)   0.0283165  0.0138929   2.038   0.0415 *
## Tu_RegimeSR2 -0.0000653  0.0208393  -0.003   0.9975  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
simulationOutput <- simulateResiduals(fittedModel = intra_tu_an_1, plot = F, )
plot(simulationOutput) #no problem
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.25. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.5. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.75. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.

intra_te_an_1<-glmmTMB(Te_intra~Te_Regime, data=subset(param_all_w0, Environment=="N"& Tu_Regime=="SR1"))
intra_te_an_2<-glmmTMB(Te_intra+1~Te_Regime, data=subset(param_all_w0, Environment=="N"& Tu_Regime=="SR1"), family=Gamma(link="log"))
intra_te_an_3<-glmmTMB(Te_intra+1~Te_Regime, data=subset(param_all_w0, Environment=="N"& Tu_Regime=="SR1"), family=gaussian(link="log"))
anova(intra_te_an_1,intra_te_an_2,intra_te_an_3)
## Data: subset(param_all_w0, Environment == "N" & Tu_Regime == "SR1")
## Models:
## intra_te_an_1: Te_intra ~ Te_Regime, zi=~0, disp=~1
## intra_te_an_2: Te_intra + 1 ~ Te_Regime, zi=~0, disp=~1
## intra_te_an_3: Te_intra + 1 ~ Te_Regime, zi=~0, disp=~1
##               Df     AIC     BIC logLik deviance  Chisq Chi Df Pr(>Chisq)    
## intra_te_an_1  3 -40.712 -39.805 23.356  -46.712                             
## intra_te_an_2  3 -40.562 -39.654 23.281  -46.562 0.0000      0          1    
## intra_te_an_3  3 -40.712 -39.805 23.356  -46.712 0.1508      0     <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(intra_te_an_3)
##  Family: gaussian  ( log )
## Formula:          Te_intra + 1 ~ Te_Regime
## Data: subset(param_all_w0, Environment == "N" & Tu_Regime == "SR1")
## 
##      AIC      BIC   logLik deviance df.resid 
##    -40.7    -39.8     23.4    -46.7        7 
## 
## 
## Dispersion estimate for gaussian family (sigma^2): 0.000548 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)  
## (Intercept)   0.01862    0.01028   1.812   0.0699 .
## Te_RegimeSR5  0.01732    0.01441   1.202   0.2294  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(intra_te_an_1)
##  Family: gaussian  ( identity )
## Formula:          Te_intra ~ Te_Regime
## Data: subset(param_all_w0, Environment == "N" & Tu_Regime == "SR1")
## 
##      AIC      BIC   logLik deviance df.resid 
##    -40.7    -39.8     23.4    -46.7        7 
## 
## 
## Dispersion estimate for gaussian family (sigma^2): 0.000548 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)  
## (Intercept)   0.01880    0.01047   1.796   0.0726 .
## Te_RegimeSR5  0.01780    0.01481   1.202   0.2294  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
simulationOutput <- simulateResiduals(fittedModel = intra_te_an_1, plot = F, )
plot(simulationOutput)# no problem
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.25. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.5. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.
## Warning in smooth.construct.tp.smooth.spec(object, dk$data, dk$knots): basis dimension, k, increased to minimum possible
## Unable to calculate quantile regression for quantile 0.75. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.

## inter

inter_tu_an_1<-glmmTMB(Tu_inter~Tu_Regime*Te_Regime, data=subset(param_all_w0, Environment=="N"))
inter_tu_an_2<-glmmTMB(Tu_inter+1~Tu_Regime*Te_Regime, data=subset(param_all_w0, Environment=="N"), family=Gamma(link="log"))
inter_tu_an_3<-glmmTMB(Tu_inter+1~Tu_Regime*Te_Regime, data=subset(param_all_w0, Environment=="N"), family=gaussian(link="log"))
anova(inter_tu_an_1,inter_tu_an_2,inter_tu_an_3)
## Data: subset(param_all_w0, Environment == "N")
## Models:
## inter_tu_an_1: Tu_inter ~ Tu_Regime * Te_Regime, zi=~0, disp=~1
## inter_tu_an_2: Tu_inter + 1 ~ Tu_Regime * Te_Regime, zi=~0, disp=~1
## inter_tu_an_3: Tu_inter + 1 ~ Tu_Regime * Te_Regime, zi=~0, disp=~1
##               Df     AIC     BIC logLik deviance  Chisq Chi Df Pr(>Chisq)    
## inter_tu_an_1  5 -66.934 -62.482 38.467  -76.934                             
## inter_tu_an_2  5 -66.587 -62.135 38.293  -76.587 0.0000      0          1    
## inter_tu_an_3  5 -66.934 -62.482 38.467  -76.934 0.3473      0     <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(inter_tu_an_3)
##  Family: gaussian  ( log )
## Formula:          Tu_inter + 1 ~ Tu_Regime * Te_Regime
## Data: subset(param_all_w0, Environment == "N")
## 
##      AIC      BIC   logLik deviance df.resid 
##    -66.9    -62.5     38.5    -76.9       13 
## 
## 
## Dispersion estimate for gaussian family (sigma^2): 0.000815 
## 
## Conditional model:
##                            Estimate Std. Error z value Pr(>|z|)   
## (Intercept)                0.039664   0.012273   3.232  0.00123 **
## Tu_RegimeSR2               0.002957   0.018379   0.161  0.87218   
## Te_RegimeSR5              -0.009884   0.017443  -0.567  0.57093   
## Tu_RegimeSR2:Te_RegimeSR5 -0.017747   0.026253  -0.676  0.49903   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(inter_tu_an_1)
##  Family: gaussian  ( identity )
## Formula:          Tu_inter ~ Tu_Regime * Te_Regime
## Data: subset(param_all_w0, Environment == "N")
## 
##      AIC      BIC   logLik deviance df.resid 
##    -66.9    -62.5     38.5    -76.9       13 
## 
## 
## Dispersion estimate for gaussian family (sigma^2): 0.000815 
## 
## Conditional model:
##                            Estimate Std. Error z value Pr(>|z|)   
## (Intercept)                0.040461   0.012769   3.169  0.00153 **
## Tu_RegimeSR2               0.003081   0.019154   0.161  0.87220   
## Te_RegimeSR5              -0.010234   0.018058  -0.567  0.57092   
## Tu_RegimeSR2:Te_RegimeSR5 -0.018206   0.027088  -0.672  0.50150   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
simulationOutput <- simulateResiduals(fittedModel = inter_tu_an_1, plot = F, )
plot(simulationOutput) # no problem

pairs(emmeans(inter_tu_an_1, pairwise~Te_Regime:Tu_Regime), adjust="none")
##  contrast          estimate     SE df t.ratio p.value
##  SR4 SR1 - SR5 SR1  0.01023 0.0181 13   0.567  0.5806
##  SR4 SR1 - SR4 SR2 -0.00308 0.0192 13  -0.161  0.8747
##  SR4 SR1 - SR5 SR2  0.02536 0.0192 13   1.324  0.2083
##  SR5 SR1 - SR4 SR2 -0.01331 0.0192 13  -0.695  0.4992
##  SR5 SR1 - SR5 SR2  0.01513 0.0192 13   0.790  0.4439
##  SR4 SR2 - SR5 SR2  0.02844 0.0202 13   1.409  0.1824
inter_te_an_1<-glmmTMB(Te_inter~Te_Regime*Tu_Regime, data=subset(param_all_w0, Environment=="N"))
inter_te_an_2<-glmmTMB(Te_inter+1~Te_Regime*Tu_Regime, data=subset(param_all_w0, Environment=="N"), family=Gamma(link="log"))
inter_te_an_3<-glmmTMB(Te_inter+1~Te_Regime*Tu_Regime, data=subset(param_all_w0, Environment=="N"), family=gaussian(link="log"))
anova(inter_te_an_1,inter_te_an_2,inter_te_an_3)
## Data: subset(param_all_w0, Environment == "N")
## Models:
## inter_te_an_1: Te_inter ~ Te_Regime * Tu_Regime, zi=~0, disp=~1
## inter_te_an_2: Te_inter + 1 ~ Te_Regime * Tu_Regime, zi=~0, disp=~1
## inter_te_an_3: Te_inter + 1 ~ Te_Regime * Tu_Regime, zi=~0, disp=~1
##               Df     AIC    BIC logLik deviance  Chisq Chi Df Pr(>Chisq)    
## inter_te_an_1  5 -35.652 -31.20 22.826  -45.652                             
## inter_te_an_2  5 -37.001 -32.55 23.501  -47.001 1.3491      0     <2e-16 ***
## inter_te_an_3  5 -35.652 -31.20 22.826  -45.652 0.0000      0          1    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(inter_te_an_2)
##  Family: Gamma  ( log )
## Formula:          Te_inter + 1 ~ Te_Regime * Tu_Regime
## Data: subset(param_all_w0, Environment == "N")
## 
##      AIC      BIC   logLik deviance df.resid 
##    -37.0    -32.5     23.5    -47.0       13 
## 
## 
## Dispersion estimate for Gamma family (sigma^2): 0.00363 
## 
## Conditional model:
##                            Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                0.101837   0.026940   3.780 0.000157 ***
## Te_RegimeSR5               0.014480   0.038099   0.380 0.703903    
## Tu_RegimeSR2              -0.046878   0.040410  -1.160 0.246022    
## Te_RegimeSR5:Tu_RegimeSR2 -0.009634   0.057148  -0.169 0.866126    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(inter_te_an_1)
##  Family: gaussian  ( identity )
## Formula:          Te_inter ~ Te_Regime * Tu_Regime
## Data: subset(param_all_w0, Environment == "N")
## 
##      AIC      BIC   logLik deviance df.resid 
##    -35.7    -31.2     22.8    -45.7       13 
## 
## 
## Dispersion estimate for gaussian family (sigma^2): 0.00464 
## 
## Conditional model:
##                           Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                0.10720    0.03045   3.521  0.00043 ***
## Te_RegimeSR5               0.01615    0.04306   0.375  0.70763    
## Tu_RegimeSR2              -0.05071    0.04567  -1.110  0.26688    
## Te_RegimeSR5:Tu_RegimeSR2 -0.01102    0.06459  -0.171  0.86456    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
pairs(emmeans(inter_te_an_1, pairwise~Te_Regime:Tu_Regime), adjust="none")
##  contrast          estimate     SE df t.ratio p.value
##  SR4 SR1 - SR5 SR1 -0.01615 0.0431 13  -0.375  0.7137
##  SR4 SR1 - SR4 SR2  0.05071 0.0457 13   1.110  0.2870
##  SR4 SR1 - SR5 SR2  0.04557 0.0457 13   0.998  0.3365
##  SR5 SR1 - SR4 SR2  0.06685 0.0457 13   1.464  0.1670
##  SR5 SR1 - SR5 SR2  0.06172 0.0457 13   1.351  0.1996
##  SR4 SR2 - SR5 SR2 -0.00513 0.0481 13  -0.107  0.9167
simulationOutput <- simulateResiduals(fittedModel = inter_te_an_1, plot = F, )
plot(simulationOutput) # no problems

inter_te_an_1_2<-glmmTMB(Te_inter~Te_Regime+Tu_Regime, data=subset(param_all_w0, Environment=="N"))

summary(inter_te_an_1_2)
##  Family: gaussian  ( identity )
## Formula:          Te_inter ~ Te_Regime + Tu_Regime
## Data: subset(param_all_w0, Environment == "N")
## 
##      AIC      BIC   logLik deviance df.resid 
##    -37.6    -34.1     22.8    -45.6       14 
## 
## 
## Dispersion estimate for gaussian family (sigma^2): 0.00464 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)   0.10965    0.02687   4.080  4.5e-05 ***
## Te_RegimeSR5  0.01125    0.03212   0.350    0.726    
## Tu_RegimeSR2 -0.05621    0.03232  -1.739    0.082 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
pairs(emmeans(inter_te_an_1_2, pairwise~Te_Regime+Tu_Regime), adjust="none")
##  contrast          estimate     SE df t.ratio p.value
##  SR4 SR1 - SR5 SR1  -0.0113 0.0321 14  -0.350  0.7313
##  SR4 SR1 - SR4 SR2   0.0562 0.0323 14   1.739  0.1039
##  SR4 SR1 - SR5 SR2   0.0450 0.0456 14   0.987  0.3405
##  SR5 SR1 - SR4 SR2   0.0675 0.0456 14   1.481  0.1609
##  SR5 SR1 - SR5 SR2   0.0562 0.0323 14   1.739  0.1039
##  SR4 SR2 - SR5 SR2  -0.0113 0.0321 14  -0.350  0.7313
Summary
summary(gr_tu_an_2)
##  Family: Gamma  ( log )
## Formula:          Tu_lambda ~ Tu_Regime
## Data: subset(param_all_w0, Environment == "N" & Te_Regime == "SR4")
## 
##      AIC      BIC   logLik deviance df.resid 
##     18.6     19.2     -6.3     12.6        6 
## 
## 
## Dispersion estimate for Gamma family (sigma^2): 0.0372 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)   0.92178    0.08625  10.688   <2e-16 ***
## Tu_RegimeSR2  0.04502    0.12937   0.348    0.728    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(gr_te_an_2)
##  Family: Gamma  ( log )
## Formula:          Te_lambda ~ Te_Regime
## Data: subset(param_all_w0, Environment == "N" & Tu_Regime == "SR1")
## 
##      AIC      BIC   logLik deviance df.resid 
##     31.7     32.6    -12.8     25.7        7 
## 
## 
## Dispersion estimate for Gamma family (sigma^2): 0.0283 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)   1.74354    0.07529  23.157   <2e-16 ***
## Te_RegimeSR5 -0.17262    0.10648  -1.621    0.105    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(intra_tu_an_1)
##  Family: gaussian  ( identity )
## Formula:          Tu_intra ~ Tu_Regime
## Data: subset(param_all_w0, Environment == "N" & Te_Regime == "SR4")
## 
##      AIC      BIC   logLik deviance df.resid 
##    -30.9    -30.4     18.5    -36.9        6 
## 
## 
## Dispersion estimate for gaussian family (sigma^2): 0.000965 
## 
## Conditional model:
##                Estimate Std. Error z value Pr(>|z|)  
## (Intercept)   0.0283165  0.0138929   2.038   0.0415 *
## Tu_RegimeSR2 -0.0000653  0.0208393  -0.003   0.9975  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(intra_te_an_1)
##  Family: gaussian  ( identity )
## Formula:          Te_intra ~ Te_Regime
## Data: subset(param_all_w0, Environment == "N" & Tu_Regime == "SR1")
## 
##      AIC      BIC   logLik deviance df.resid 
##    -40.7    -39.8     23.4    -46.7        7 
## 
## 
## Dispersion estimate for gaussian family (sigma^2): 0.000548 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)  
## (Intercept)   0.01880    0.01047   1.796   0.0726 .
## Te_RegimeSR5  0.01780    0.01481   1.202   0.2294  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
pairs(emmeans(inter_tu_an_1, pairwise~Te_Regime:Tu_Regime), adjust="none")
##  contrast          estimate     SE df t.ratio p.value
##  SR4 SR1 - SR5 SR1  0.01023 0.0181 13   0.567  0.5806
##  SR4 SR1 - SR4 SR2 -0.00308 0.0192 13  -0.161  0.8747
##  SR4 SR1 - SR5 SR2  0.02536 0.0192 13   1.324  0.2083
##  SR5 SR1 - SR4 SR2 -0.01331 0.0192 13  -0.695  0.4992
##  SR5 SR1 - SR5 SR2  0.01513 0.0192 13   0.790  0.4439
##  SR4 SR2 - SR5 SR2  0.02844 0.0202 13   1.409  0.1824
pairs(emmeans(inter_te_an_1, pairwise~Te_Regime:Tu_Regime), adjust="none")
##  contrast          estimate     SE df t.ratio p.value
##  SR4 SR1 - SR5 SR1 -0.01615 0.0431 13  -0.375  0.7137
##  SR4 SR1 - SR4 SR2  0.05071 0.0457 13   1.110  0.2870
##  SR4 SR1 - SR5 SR2  0.04557 0.0457 13   0.998  0.3365
##  SR5 SR1 - SR4 SR2  0.06685 0.0457 13   1.464  0.1670
##  SR5 SR1 - SR5 SR2  0.06172 0.0457 13   1.351  0.1996
##  SR4 SR2 - SR5 SR2 -0.00513 0.0481 13  -0.107  0.9167
Anova(gr_tu_an_2)
## Analysis of Deviance Table (Type II Wald chisquare tests)
## 
## Response: Tu_lambda
##            Chisq Df Pr(>Chisq)
## Tu_Regime 0.1211  1     0.7278
Anova(gr_te_an_2)
## Analysis of Deviance Table (Type II Wald chisquare tests)
## 
## Response: Te_lambda
##            Chisq Df Pr(>Chisq)
## Te_Regime 2.6282  1      0.105
Anova(intra_tu_an_1)
## Analysis of Deviance Table (Type II Wald chisquare tests)
## 
## Response: Tu_intra
##           Chisq Df Pr(>Chisq)
## Tu_Regime     0  1     0.9975
Anova(intra_te_an_1)
## Analysis of Deviance Table (Type II Wald chisquare tests)
## 
## Response: Te_intra
##            Chisq Df Pr(>Chisq)
## Te_Regime 1.4447  1     0.2294
Anova(inter_tu_an_1, type=3)
## Analysis of Deviance Table (Type III Wald chisquare tests)
## 
## Response: Tu_inter
##                       Chisq Df Pr(>Chisq)   
## (Intercept)         10.0403  1   0.001532 **
## Tu_Regime            0.0259  1   0.872203   
## Te_Regime            0.3211  1   0.570918   
## Tu_Regime:Te_Regime  0.4518  1   0.501504   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Anova(inter_te_an_1, type=3)
## Analysis of Deviance Table (Type III Wald chisquare tests)
## 
## Response: Te_inter
##                       Chisq Df Pr(>Chisq)    
## (Intercept)         12.3975  1  0.0004299 ***
## Te_Regime            0.1407  1  0.7076304    
## Tu_Regime            1.2327  1  0.2668838    
## Te_Regime:Tu_Regime  0.0291  1  0.8645601    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
pairs(emmeans(inter_te_an_1, pairwise~Tu_Regime| Te_Regime), adjust="none")
## Te_Regime = SR4:
##  contrast  estimate     SE df t.ratio p.value
##  SR1 - SR2   0.0507 0.0457 13   1.110  0.2870
## 
## Te_Regime = SR5:
##  contrast  estimate     SE df t.ratio p.value
##  SR1 - SR2   0.0617 0.0457 13   1.351  0.1996

3 - Predicting coexistence (structural stability)

3.1 - Structural stability

Defining functions

The structural stability approach takes a LV, in the appendix we show how to expand to other type of model_w0s mostly a Beverton Holt function, we did not explore the ricker function, but we suspect it will work equally good, So no worries, we are good to go. Regarding the function to calculate structural niche and fitness differences, These are the functions (omega is niche differences) (theta is fitness differences). For calculating theta you also need to calculate the centroid. The function test feasibility is to know whether a species combination can or can not coexist.

#input parameters:
#alpha = competition strenght matrix 
#r = vector of intrinsic growth rates

#structural niche difference (output on a log scale)
Omega <- function(alpha){
  n <- nrow(alpha)
  Sigma <-solve(t(alpha) %*% alpha, tol = 1e-40)
  d <- pmvnorm(lower = rep(0,n), upper = rep(Inf,n), mean = rep(0,n), sigma = Sigma)
  out <- log10(d[1]) + n * log10(2)
  return(out) 
}

#vector defining the centroid of the feasibility domain
r_centroid <- function(alpha){
  n <- nrow(alpha)
  D <- diag(1/sqrt(diag(t(alpha)%*%alpha)))
  alpha_n <- alpha %*% D
  r_c <- rowSums(alpha_n) /n 
  r_c <- t(t(r_c))
  return(r_c)
}


#structural fitness difference (in degree)
theta <- function(alpha,r){
  r_c <- r_centroid(alpha)
  out <- acos(sum(r_c*r, na.rm = TRUE)/(sqrt(sum(r^2, na.rm = TRUE))*sqrt(sum(r_c^2, na.rm = TRUE))))*90/pi
  return(out)
}


#test if a system (alpha and r) is feasible (output 1 = feasible, 0 = not feasible)
test_feasibility <- function(alpha,r){
  out <- prod(solve(alpha,r)>0)
  return(out)
}

3.1.1 - estimating structural stability for all replicates

#x<-2
struct_mat_REP<-as.data.frame(t(as.data.frame(sapply(c(1:length(param_all_REP[,1])), function(x){
  #print(x)
    aux_alpha<-matrix(c(param_all_REP$Te_intra[x],param_all_REP$Te_inter[x],param_all_REP$Tu_inter[x], param_all_REP$Tu_intra[x]), ncol=2, byrow=TRUE)
  aux_lambda<-c(param_all_REP$Te_lambda[x],param_all_REP$Tu_lambda[x])
  
  om<-Omega(aux_alpha)
  tta<-theta(aux_alpha, aux_lambda)
  feas<- test_feasibility(aux_alpha, aux_lambda)
  
  c(om, tta, feas)
}))))


colnames(struct_mat_REP)<-c("ND", "FD", "Feasibility")

#For the lower we use the higher alphas with lower lambda, and for upper the other way around
# Since we have facilitation we have to actually test what is the lowest value

struct_mat_REP_U<-as.data.frame(t(as.data.frame(sapply(c(1:length(param_all_REP_lower[,1])), function(x){
  #print(x)
    aux_alpha<-matrix(c(param_all_REP_upper$Te_intra[x],param_all_REP_upper$Te_inter[x], param_all_REP_upper$Tu_inter[x],param_all_REP_upper$Tu_intra[x]), ncol=2, byrow=TRUE)
  aux_lambda<-c(param_all_REP_upper$Te_lambda[x],param_all_REP_upper$Tu_lambda[x] )
  
  om<-Omega(aux_alpha)
  tta<-theta(aux_alpha, aux_lambda)
  feas<- test_feasibility(aux_alpha, aux_lambda)
  
  c(om, tta, feas)
}))))


struct_mat_REP_L<-as.data.frame(t(as.data.frame(sapply(c(1:length(param_all_REP_upper[,1])), function(x){
  #print(x)
    aux_alpha<-matrix(c(param_all_REP_lower$Te_intra[x],param_all_REP_lower$Te_inter[x],param_all_REP_lower$Tu_inter[x],param_all_REP_lower$Tu_intra[x]), ncol=2, byrow=TRUE)
  aux_lambda<-c(param_all_REP_lower$Te_lambda[x],param_all_REP_lower$Tu_lambda[x] )
  
  om<-Omega(aux_alpha)
  tta<-theta(aux_alpha, aux_lambda)
  feas<- test_feasibility(aux_alpha, aux_lambda)
  
  c(om, tta, feas)
}))))

colnames(struct_mat_REP_U)<-c("ND_U", "FD_U", "Feasibility_U")
colnames(struct_mat_REP_L)<-c("ND_L", "FD_L", "Feasibility_L")

struct_mat_REP<-cbind(param_all_REP, struct_mat_REP,struct_mat_REP_L,struct_mat_REP_U)

# To create the boundaries
bound_struct_rk_w0<-data.frame(ND=seq(0,1, 0.01))
bound_struct_rk_w0$FD<-45*bound_struct_rk_w0$ND

struct_mat_REP3<-struct_mat_REP

3.1.2 - estimating structural stability per replicate

struct_mat_w0<-as.data.frame(t(as.data.frame(sapply(c(1:length(param_all_w0[,1])), function(x){
  #print(x)
    aux_alpha<-matrix(c(param_all_w0$Te_intra[x],param_all_w0$Te_inter[x],param_all_w0$Tu_inter[x], param_all_w0$Tu_intra[x]), ncol=2, byrow=TRUE)
  aux_lambda<-c(param_all_w0$Te_lambda[x],param_all_w0$Tu_lambda[x] )
  
  om<-Omega(aux_alpha)
  tta<-theta(aux_alpha, aux_lambda)
  feas<- test_feasibility(aux_alpha, aux_lambda)
  
  c(om, tta, feas)
}))))

colnames(struct_mat_w0)<-c("ND", "FD", "Feasibility")

struct_mat_w0_L<-as.data.frame(t(as.data.frame(sapply(c(1:length(param_all_w0_lower[,1])), function(x){
  #print(x)
    aux_alpha<-matrix(c(param_all_w0_upper$Te_intra[x],param_all_w0_upper$Te_inter[x],param_all_w0_upper$Tu_inter[x], param_all_w0_upper$Tu_intra[x]), ncol=2, byrow=TRUE)
  aux_lambda<-c(param_all_w0_lower$Te_lambda[x],param_all_w0_lower$Tu_lambda[x] )
  
  om<-Omega(aux_alpha)
  tta<-theta(aux_alpha, aux_lambda)
  feas<- test_feasibility(aux_alpha, aux_lambda)
  
  c(om, tta, feas)
}))))

colnames(struct_mat_w0_L)<-c("ND_L", "FD_L", "Feasibility_L")

struct_mat_w0_U<-as.data.frame(t(as.data.frame(sapply(c(1:length(param_all_w0_upper[,1])), function(x){
  #print(x)
    aux_alpha<-matrix(c(param_all_w0_lower$Te_intra[x],param_all_w0_lower$Te_inter[x],param_all_w0_lower$Tu_inter[x], param_all_w0_lower$Tu_intra[x]), ncol=2, byrow=TRUE)
  aux_lambda<-c(param_all_w0_upper$Te_lambda[x],param_all_w0_upper$Tu_lambda[x] )
  
  om<-Omega(aux_alpha)
  tta<-theta(aux_alpha, aux_lambda)
  feas<- test_feasibility(aux_alpha, aux_lambda)
  
  c(om, tta, feas)
}))))

colnames(struct_mat_w0_U)<-c("ND_U", "FD_U", "Feasibility_U")

struct_mat_w0<-cbind(param_all_w0, struct_mat_w0,struct_mat_w0_L,struct_mat_w0_U)

bound_struct_rk_w0<-data.frame(ND=seq(0,1, 0.01))
bound_struct_rk_w0$FD<-45*bound_struct_rk_w0$ND

3.2 - Distance to the edge and who wins

struct_mat_REP$a21_a11<-struct_mat_REP$Te_inter/struct_mat_REP$Tu_intra
struct_mat_REP$a22_a12<-struct_mat_REP$Te_intra/struct_mat_REP$Tu_inter

## Now to calculate the upper and lower bounds we have to see which is the lowest value of competition (and those create the upper bounds) or the highest values of competition (those create the lower boundaries)

struct_mat_REP$a21_a11_upper<-param_all_REP_lower$Te_inter/param_all_REP_lower$Tu_intra
struct_mat_REP$a22_a12_upper<-param_all_REP_lower$Te_intra/param_all_REP_lower$Tu_inter

struct_mat_REP$a21_a11_lower<-param_all_REP_upper$Te_inter/param_all_REP_upper$Tu_intra
struct_mat_REP$a22_a12_lower<-param_all_REP_upper$Te_intra/param_all_REP_upper$Tu_inter

struct_mat_REP$Tu_lambda_lower<-param_all_REP_lower$Tu_lambda
struct_mat_REP$Te_lambda_lower<-param_all_REP_lower$Te_lambda
struct_mat_REP$Tu_lambda_upper<-param_all_REP_upper$Tu_lambda
struct_mat_REP$Te_lambda_upper<-param_all_REP_upper$Te_lambda

Final figure arrows

struct_mat_REP$min_a21_a11<-sapply(c(1:dim(struct_mat_REP)[1]), function(x){
  min(c(struct_mat_REP$a21_a11_lower[x],struct_mat_REP$a21_a11_upper[x]))})

struct_mat_REP$min_a22_a12<-sapply(c(1:dim(struct_mat_REP)[1]), function(x){
  min(c(struct_mat_REP$a22_a12_lower[x],struct_mat_REP$a22_a12_upper[x]))})

struct_mat_REP$max_a21_a11<-sapply(c(1:dim(struct_mat_REP)[1]), function(x){
  max(c(struct_mat_REP$a21_a11_lower[x],struct_mat_REP$a21_a11_upper[x]))})

struct_mat_REP$max_a22_a12<-sapply(c(1:dim(struct_mat_REP)[1]), function(x){
  max(c(struct_mat_REP$a22_a12_lower[x],struct_mat_REP$a22_a12_upper[x]))})

#write.csv(struct_mat_REP, "Analyses/structural_REP.csv")

per replicate

struct_mat_w0$a21_a11<-struct_mat_w0$Te_inter/struct_mat_w0$Tu_intra
struct_mat_w0$a22_a12<-struct_mat_w0$Te_intra/struct_mat_w0$Tu_inter

struct_mat_w0$a21_a11_lower<-param_all_w0_lower$Te_inter/param_all_w0_lower$Tu_intra
struct_mat_w0$a22_a12_lower<-param_all_w0_lower$Te_intra/param_all_w0_lower$Tu_inter

struct_mat_w0$a21_a11_upper<-param_all_w0_upper$Te_inter/param_all_w0_upper$Tu_intra
struct_mat_w0$a22_a12_upper<-param_all_w0_upper$Te_intra/param_all_w0_upper$Tu_inter

#write.csv(struct_mat_w0, "Analyses/structural_REP_w0.csv")

Estimating distance to the edge

Importing to prevent problems with reading information

struct_mat_REP_final<-read.csv("./Analyses/structural_REP.csv")
struct_mat_REP_final<-struct_mat_REP_final[,-1]

struct_mat_w0<-read.csv("./Analyses/structural_REP_w0.csv")
struct_mat_w0<-struct_mat_w0[,-1]

Testing difference to one of the edges of the cone

all replicates
# calculating y for the x corresponding to the lambda Tu, in the vector slope
struct_mat_REP$Tu_lambda[1]*struct_mat_REP$a21_a11[1]
## [1] 7.247462
# just to be sure, it is equivalent to use the Te or Tu lambda
acos(Dot(LSAfun::normalize(c(struct_mat_REP$Tu_lambda[1], struct_mat_REP$Te_lambda[1]))
,LSAfun::normalize(c(struct_mat_REP$Tu_lambda[1],struct_mat_REP$Tu_lambda[1]*struct_mat_REP$a21_a11[1]))))
## [1] 0.09134927
acos(Dot(LSAfun::normalize(c(struct_mat_REP$Tu_lambda[1], struct_mat_REP$Te_lambda[1]))
,LSAfun::normalize(c(struct_mat_REP$Te_lambda[1]/struct_mat_REP$a21_a11[1], struct_mat_REP$Te_lambda[1]))))
## [1] 0.09134927
#And if I use a random value of 10
acos(Dot(LSAfun::normalize(c(struct_mat_REP$Tu_lambda[1], struct_mat_REP$Te_lambda[1])),
LSAfun::normalize(c(10,10*struct_mat_REP$a21_a11[1]))))
## [1] 0.09134927
# also ok, so I can just use the lambda's to do this

struct_mat_REP$distanceTu<-sapply(c(1:length(struct_mat_REP$ND)), function(x) acos(Dot(LSAfun::normalize(c(struct_mat_REP$Tu_lambda[x], struct_mat_REP$Te_lambda[x]))
,LSAfun::normalize(c(struct_mat_REP$Tu_lambda[x],struct_mat_REP$Tu_lambda[x]*struct_mat_REP$a21_a11[x])))))

struct_mat_REP$distanceTe<-sapply(c(1:length(struct_mat_REP$ND)), function(x) acos(Dot(LSAfun::normalize(c(struct_mat_REP$Tu_lambda[x], struct_mat_REP$Te_lambda[x]))
,LSAfun::normalize(c(struct_mat_REP$Te_lambda[x]/struct_mat_REP$a22_a12[x],struct_mat_REP$Te_lambda[x])))))


struct_mat_REP$distanceTu_lower<-sapply(c(1:length(struct_mat_REP$ND)), function(x) acos(Dot(LSAfun::normalize(c(struct_mat_REP$Tu_lambda_lower[x], struct_mat_REP$Te_lambda_lower[x]))
,LSAfun::normalize(c(struct_mat_REP$Tu_lambda_lower[x],struct_mat_REP$Tu_lambda_lower[x]*struct_mat_REP$a21_a11_lower[x])))))

struct_mat_REP$distanceTu_upper<-sapply(c(1:length(struct_mat_REP$ND)), function(x) acos(Dot(LSAfun::normalize(c(struct_mat_REP$Tu_lambda_upper[x], struct_mat_REP$Te_lambda_upper[x]))
,LSAfun::normalize(c(struct_mat_REP$Tu_lambda_upper[x],struct_mat_REP$Tu_lambda_upper[x]*struct_mat_REP$a21_a11_upper[x])))))

struct_mat_REP$distanceTe_lower<-sapply(c(1:length(struct_mat_REP$ND)), function(x) acos(Dot(LSAfun::normalize(c(struct_mat_REP$Tu_lambda_lower[x], struct_mat_REP$Te_lambda_lower[x]))
,LSAfun::normalize(c(struct_mat_REP$Te_lambda_lower[x]/struct_mat_REP$a22_a12_lower[x],struct_mat_REP$Te_lambda_lower[x])))))

struct_mat_REP$distanceTe_upper<-sapply(c(1:length(struct_mat_REP$ND)), function(x) acos(Dot(LSAfun::normalize(c(struct_mat_REP$Tu_lambda_upper[x], struct_mat_REP$Te_lambda_upper[x]))
,LSAfun::normalize(c(struct_mat_REP$Te_lambda_upper[x]/struct_mat_REP$a22_a12_upper[x],struct_mat_REP$Te_lambda_upper[x])))))
per replicate
# calculating y for the x corresponding to the lambda Tu, in the vector slope
struct_mat_w0$Tu_lambda[1]*struct_mat_w0$a21_a11[1]
## [1] 5.059375
# just to be sure, it is equivalent to use the Te or Tu lambda
acos(Dot(LSAfun::normalize(c(struct_mat_w0$Tu_lambda[1], struct_mat_w0$Te_lambda[1]))
,LSAfun::normalize(c(struct_mat_w0$Tu_lambda[1],struct_mat_w0$Tu_lambda[1]*struct_mat_w0$a21_a11[1]))))
## [1] 0.01325358
acos(Dot(LSAfun::normalize(c(struct_mat_w0$Tu_lambda[1], struct_mat_w0$Te_lambda[1]))
,LSAfun::normalize(c(struct_mat_w0$Te_lambda[1]/struct_mat_w0$a21_a11[1], struct_mat_w0$Te_lambda[1]))))
## [1] 0.01325358
#And if I use a random value of 10
acos(Dot(LSAfun::normalize(c(struct_mat_w0$Tu_lambda[1], struct_mat_w0$Te_lambda[1])),
LSAfun::normalize(c(10,10*struct_mat_w0$a21_a11[1]))))
## [1] 0.01325358
# also ok, so I can just use the lambda's to do this

struct_mat_w0$distanceTu<-sapply(c(1:length(struct_mat_w0$ND)), function(x) acos(Dot(LSAfun::normalize(c(struct_mat_w0$Tu_lambda[x], struct_mat_w0$Te_lambda[x]))
,LSAfun::normalize(c(struct_mat_w0$Tu_lambda[x],struct_mat_w0$Tu_lambda[x]*struct_mat_w0$a21_a11[x])))))

struct_mat_w0$distanceTe<-sapply(c(1:length(struct_mat_w0$ND)), function(x) acos(Dot(LSAfun::normalize(c(struct_mat_w0$Tu_lambda[x], struct_mat_w0$Te_lambda[x]))
,LSAfun::normalize(c(struct_mat_w0$Te_lambda[x]/struct_mat_w0$a22_a12[x],struct_mat_w0$Te_lambda[x])))))

struct_mat_w0$distanceTu_lower<-sapply(c(1:length(struct_mat_w0$ND)), function(x) acos(Dot(LSAfun::normalize(c(struct_mat_w0$Tu_lambda_lower[x], struct_mat_w0$Te_lambda_lower[x]))
,LSAfun::normalize(c(struct_mat_w0$Tu_lambda_lower[x],struct_mat_w0$Tu_lambda_lower[x]*struct_mat_w0$a21_a11_lower[x])))))

struct_mat_w0$distanceTu_upper<-sapply(c(1:length(struct_mat_w0$ND)), function(x) acos(Dot(LSAfun::normalize(c(struct_mat_w0$Tu_lambda_upper[x], struct_mat_w0$Te_lambda_upper[x]))
,LSAfun::normalize(c(struct_mat_w0$Tu_lambda_upper[x],struct_mat_w0$Tu_lambda_upper[x]*struct_mat_w0$a21_a11_upper[x])))))

struct_mat_w0$distanceTe_lower<-sapply(c(1:length(struct_mat_w0$ND)), function(x) acos(Dot(LSAfun::normalize(c(struct_mat_w0$Tu_lambda_lower[x], struct_mat_w0$Te_lambda_lower[x]))
,LSAfun::normalize(c(struct_mat_w0$Te_lambda_lower[x]/struct_mat_w0$a22_a12_lower[x],struct_mat_w0$Te_lambda_lower[x])))))

struct_mat_w0$distanceTe_upper<-sapply(c(1:length(struct_mat_w0$ND)), function(x) acos(Dot(LSAfun::normalize(c(struct_mat_w0$Tu_lambda_upper[x], struct_mat_w0$Te_lambda_upper[x]))
,LSAfun::normalize(c(struct_mat_w0$Te_lambda_upper[x]/struct_mat_w0$a22_a12_upper[x],struct_mat_w0$Te_lambda_upper[x])))))

# Putting distance as negative if the system is unfeasible (i.e. if there is no coexistence, because then they are outside of the feasibility cone)
struct_mat_w0$distanceTu2<-sapply(c(1:length(struct_mat_w0$ND)), function(x){
  if(struct_mat_w0$Feasibility[x]==0)
    a<-struct_mat_w0$distanceTu[x]*-1
  else
    a<-struct_mat_w0$distanceTu[x]
  
  a
  })

struct_mat_w0$distanceTe2<-sapply(c(1:length(struct_mat_w0$ND)), function(x){
  if(struct_mat_w0$Feasibility[x]==0)
    a<-struct_mat_w0$distanceTe[x]*-1
  else
    a<-struct_mat_w0$distanceTe[x]
  
  a
  })

struct_mat_REP$distanceTu2<-sapply(c(1:length(struct_mat_REP$ND)), function(x){
  if(struct_mat_REP$Feasibility[x]==0)
    a<-struct_mat_REP$distanceTu[x]*-1
  else
    a<-struct_mat_REP$distanceTu[x]
  
  a
  })

struct_mat_REP$distanceTe2<-sapply(c(1:length(struct_mat_REP$ND)), function(x){
  if(struct_mat_REP$Feasibility[x]==0)
    a<-struct_mat_REP$distanceTe[x]*-1
  else
    a<-struct_mat_REP$distanceTe[x]
  
  a
  })

#lower and upper bounds

struct_mat_w0$distanceTu2_lower<-sapply(c(1:length(struct_mat_w0$ND)), function(x){
  if(struct_mat_w0$Feasibility_L[x]==0)
    a<-struct_mat_w0$distanceTu_lower[x]*-1
  else
    a<-struct_mat_w0$distanceTu_lower[x]
  
  a
  })

struct_mat_w0$distanceTe2_lower<-sapply(c(1:length(struct_mat_w0$ND)), function(x){
  if(struct_mat_w0$Feasibility_L[x]==0)
    a<-struct_mat_w0$distanceTe_lower[x]*-1
  else
    a<-struct_mat_w0$distanceTe_lower[x]
  
  a
  })

struct_mat_w0$distanceTu2_upper<-sapply(c(1:length(struct_mat_w0$ND)), function(x){
  if(struct_mat_w0$Feasibility_L[x]==0)
    a<-struct_mat_w0$distanceTu_upper[x]*-1
  else
    a<-struct_mat_w0$distanceTu_upper[x]
  
  a
  })

struct_mat_w0$distanceTe2_upper<-sapply(c(1:length(struct_mat_w0$ND)), function(x){
  if(struct_mat_w0$Feasibility_L[x]==0)
    a<-struct_mat_w0$distanceTe_upper[x]*-1
  else
    a<-struct_mat_w0$distanceTe_upper[x]
  
  a
  })

struct_mat_REP$distanceTu2_upper<-sapply(c(1:length(struct_mat_REP$ND)), function(x){
  if(struct_mat_REP$Feasibility_U[x]==0)
    a<-struct_mat_REP$distanceTu_upper[x]*-1
  else
    a<-struct_mat_REP$distanceTu_upper[x]
  
  a
  })

struct_mat_REP$distanceTe2_upper<-sapply(c(1:length(struct_mat_REP$ND)), function(x){
  if(struct_mat_REP$Feasibility_U[x]==0)
    a<-struct_mat_REP$distanceTe_upper[x]*-1
  else
    a<-struct_mat_REP$distanceTe_upper[x]
  
  a
  })


struct_mat_REP$distanceTu2_lower<-sapply(c(1:length(struct_mat_REP$ND)), function(x){
  if(struct_mat_REP$Feasibility_U[x]==0)
    a<-struct_mat_REP$distanceTu_lower[x]*-1
  else
    a<-struct_mat_REP$distanceTu_lower[x]
  
  a
  })

struct_mat_REP$distanceTe2_lower<-sapply(c(1:length(struct_mat_REP$ND)), function(x){
  if(struct_mat_REP$Feasibility_U[x]==0)
    a<-struct_mat_REP$distanceTe_lower[x]*-1
  else
    a<-struct_mat_REP$distanceTe_lower[x]
  
  a
  })
per replicate
struct_mat_w0$minDistance<-sapply(c(1:length(struct_mat_w0$ND)), function(x){
  min( c(struct_mat_w0$distanceTu[x], struct_mat_w0$distanceTe[x]))
 
})

struct_mat_w0$minDistance2<-sapply(c(1:length(struct_mat_w0$ND)), function(x){
  a<-min( c(abs(struct_mat_w0$distanceTu2[x]), abs(struct_mat_w0$distanceTe2[x])))
 
  if(struct_mat_w0$Feasibility[x]==0)
    a2<-a*-1
  else
    a2<-a
})

struct_mat_REP$minDistance2<-sapply(c(1:length(struct_mat_REP$ND)), function(x){
  a<-min( c(abs(struct_mat_REP$distanceTu2[x]), abs(struct_mat_REP$distanceTe2[x])))
  if(struct_mat_REP$Feasibility[x]==0)
     a2<-a*-1
  else
    a2<-a
})

checking which is the shortest distance

#struct_mat_REP<-struct_mat_REP[,-19]

struct_mat_REP$minDistance<-sapply(c(1:length(struct_mat_REP$ND)), function(x){
  min( c(struct_mat_REP$distanceTu[x], struct_mat_REP$distanceTe[x]))
 
})

struct_mat_w0$minDistance<-sapply(c(1:length(struct_mat_w0$ND)), function(x){
  min( c(struct_mat_w0$distanceTu[x], struct_mat_w0$distanceTe[x]))
 
})

struct_mat_REP$minDistance_L<-sapply(c(1:length(struct_mat_REP$ND)), function(x){
  a<-colnames(struct_mat_REP[x,which(struct_mat_REP[x,]==min( c(struct_mat_REP$distanceTu[x], struct_mat_REP$distanceTe[x])))])[1]
  
  if(a=="distanceTu"){
    res<- struct_mat_REP$distanceTu_lower[x]
  }else if(a=="distanceTe"){
    res<- struct_mat_REP$distanceTe_lower[x]
  }else
    res<-NA
  
  res
  })


struct_mat_REP$minDistance_U<-sapply(c(1:length(struct_mat_REP$ND)), function(x){
  a<-colnames(struct_mat_REP[x,which(struct_mat_REP[x,]==min( c(struct_mat_REP$distanceTu[x], struct_mat_REP$distanceTe[x])))])[1]
  
  if(a=="distanceTu"){
    res<- struct_mat_REP$distanceTu_upper[x]
  }else if(a=="distanceTe"){
    res<- struct_mat_REP$distanceTe_upper[x]
  }else
    res<-NA
  
  res
  })


struct_mat_w0$minDistance_L<-sapply(c(1:length(struct_mat_w0$ND)), function(x){
  a<-colnames(struct_mat_w0[x,which(struct_mat_w0[x,]==min( c(struct_mat_w0$distanceTu[x], struct_mat_w0$distanceTe[x])))])[1]
  
  if(a=="distanceTu"){
    res<- struct_mat_w0$distanceTu_lower[x]
  }else if(a=="distanceTe"){
    res<- struct_mat_w0$distanceTe_lower[x]
  }else
    res<-NA
  
  res
  })


struct_mat_w0$minDistance_U<-sapply(c(1:length(struct_mat_w0$ND)), function(x){
  a<-colnames(struct_mat_w0[x,which(struct_mat_w0[x,]==min( c(struct_mat_w0$distanceTu[x], struct_mat_w0$distanceTe[x])))])[1]
  
  if(a=="distanceTu"){
    res<- struct_mat_w0$distanceTu_upper[x]
  }else if(a=="distanceTe"){
    res<- struct_mat_w0$distanceTe_upper[x]
  }else
    res<-NA
  
  res
  })



struct_mat_w0$minDistance2_lower<-sapply(c(1:length(struct_mat_w0$ND)), function(x){
  a<-struct_mat_w0$minDistance_L[x]
 
  if(struct_mat_w0$Feasibility[x]==0)
    a2<-a*-1
  else
    a2<-a
})

struct_mat_REP$minDistance2_lower<-sapply(c(1:length(struct_mat_REP$ND)), function(x){
  a<-struct_mat_REP$minDistance_L[x]
  if(struct_mat_REP$Feasibility[x]==0)
     a2<-a*-1
  else
    a2<-a
})

struct_mat_w0$minDistance2_upper<-sapply(c(1:length(struct_mat_w0$ND)), function(x){
  a<-struct_mat_w0$minDistance_U[x]
 
  if(struct_mat_w0$Feasibility[x]==0)
    a2<-a*-1
  else
    a2<-a
})

struct_mat_REP$minDistance2_upper<-sapply(c(1:length(struct_mat_REP$ND)), function(x){
  a<-struct_mat_REP$minDistance_U[x]
  if(struct_mat_REP$Feasibility[x]==0)
     a2<-a*-1
  else
    a2<-a
})
na.omit(subset(struct_mat_w0, Environment=="Cd"))
##    Tu_Regime Te_Regime Replicate Environment Tu_lambda Te_lambda     Tu_intra
## 19       SR1       SR4         1          Cd  1.263518  2.079319  0.008968545
## 20       SR2       SR4         1          Cd  1.559691  2.079319  0.040797476
## 21       SR1       SR5         1          Cd  1.263518  2.685230  0.008968545
## 22       SR2       SR5         1          Cd  1.559691  2.685230  0.040797476
## 23       SR1       SR4         2          Cd  1.098786  1.363013 -0.000853826
## 24       SR1       SR5         2          Cd  1.098786  1.612001 -0.000853826
## 25       SR1       SR4         3          Cd  1.155278  1.980124  0.009196018
## 26       SR2       SR4         3          Cd  1.481804  1.980124  0.024641295
## 27       SR1       SR5         3          Cd  1.155278  1.876019  0.009196018
## 28       SR2       SR5         3          Cd  1.481804  1.876019  0.024641295
## 29       SR1       SR4         4          Cd  1.200719  1.597399  0.005190474
## 30       SR2       SR4         4          Cd  1.217856  1.597399  0.002009553
## 31       SR1       SR5         4          Cd  1.200719  2.287674  0.005190474
## 32       SR2       SR5         4          Cd  1.217856  2.287674  0.002009553
## 33       SR1       SR4         5          Cd  1.392517  1.741602  0.022828169
## 34       SR2       SR4         5          Cd  1.386070  1.741602 -0.016080607
## 35       SR1       SR5         5          Cd  1.392517  2.540195  0.022828169
## 36       SR2       SR5         5          Cd  1.386070  2.540195 -0.016080607
##        Te_intra      Tu_inter     Te_inter          ND        FD Feasibility
## 19  0.021943476  0.0255938201 -0.011320658  0.01059047 32.108281           0
## 20  0.021943476  0.0185628236  0.022957187 -0.64452913  6.778830           0
## 21  0.049727551  0.0161563696  0.040176078 -1.22064484  4.953829           0
## 22  0.049727551  0.0256111879  0.019650450 -0.38566557  7.808030           1
## 23 -0.010072024 -0.0035455089 -0.040243208 -0.69471029 75.715150           0
## 24  0.008329916 -0.0004215226  0.045156365 -1.69568614 18.134770           0
## 25  0.007206893 -0.0075988794  0.051910250 -0.20171454 24.248113           0
## 26  0.007206893  0.0277985348 -0.029389759 -0.14430138 35.467599           0
## 27  0.027942371 -0.0078557435  0.045986919 -0.52269958 16.911296           0
## 28  0.027942371  0.0257896361 -0.003616994 -0.20881742 16.112063           0
## 29 -0.013887492  0.0061943962 -0.055841136 -0.68174129 64.197115           0
## 30 -0.013887492 -0.0043296513  0.010301717  0.28561317 56.572495           0
## 31  0.030862480  0.0139779146  0.054868584 -0.67635311  6.404134           0
## 32  0.030862480 -0.0209888470 -0.006842631  0.25566864 71.660734           0
## 33  0.020501123  0.0333857080 -0.009528609 -0.22017331 23.453553           0
## 34  0.020501123  0.0168103044  0.003244074  0.11743723 29.068331           1
## 35  0.051710287 -0.0271574132  0.014084317 -0.01957060  6.710900           1
## 36  0.051710287  0.0018787191  0.001434420 -0.01480644 35.015123           0
##           ND_L      FD_L Feasibility_L        ND_U      FD_U Feasibility_U
## 19 -1.54462751  3.990633             0  0.04721106 53.030793             0
## 20 -2.11727214  2.439802             0  0.27834857  4.277922             1
## 21 -2.21394499  3.418906             0 -0.49340581 14.243236             0
## 22 -0.73610998  3.632260             1  0.02906109 17.316621             1
## 23 -0.02775893 31.187148             0 -0.53245541 82.830862             0
## 24 -1.18449002 13.455195             0  0.15741639 58.614527             0
## 25 -1.02687854  4.736395             0  0.09822193 46.312483             0
## 26 -0.32451735 17.008548             0 -0.45456203 58.163677             0
## 27 -1.12245717  7.389838             0 -0.14014526 34.895549             0
## 28 -0.60125687  4.455240             1  0.03285158 35.275185             0
## 29 -0.04707808 38.215311             0 -1.07420487 75.541593             0
## 30 -0.38062249  2.533284             1 -0.78537030 89.968911             0
## 31 -0.74671232  5.442735             0 -1.34364125 16.447221             0
## 32 -0.49162415  4.587629             1 -0.05262855 75.348837             0
## 33 -0.69289429 10.207231             0 -0.06234705 43.508446             0
## 34 -0.30644174  8.552267             1 -0.24996960 70.524428             0
## 35 -0.31990808  6.283201             1  0.22110741 80.832302             0
## 36 -0.68826698 10.413547             0  0.02909675 55.579969             0
##         a21_a11     a22_a12 a21_a11_lower a22_a12_lower a21_a11_upper
## 19  -1.26226253   0.8573740     9.0857011    0.07088079    1.10634567
## 20   0.56271097   1.1821195    -0.4252340   -0.62964225    1.07273088
## 21   4.47966524   3.0778914    -2.9048510    5.72984898    2.78937851
## 22   0.48165849   1.9416339    -0.4048642    3.53091672    0.93931981
## 23  47.13279520   2.8407836     6.0199143    1.38435740   -1.47044720
## 24 -52.88707823 -19.7614947    -2.5520915    1.78307147    6.61844676
## 25   5.64486195  -0.9484152    -8.9792716    0.55876803    3.25601432
## 26  -1.19270348   0.2592544    -4.4518500   -1.02618862   -0.07114558
## 27   5.00074282  -3.5569352    -9.4888928   -0.34055590    2.63386539
## 28  -0.14678586   1.0834729    -2.2200104    0.60851475    0.56666514
## 29 -10.75838893  -2.2419445    17.8416083    5.24495164   -2.13868952
## 30   5.12637107   3.2075314     1.0340694    1.78287601    2.20746540
## 31  10.57101640   2.2079459    -6.5835829  -12.54561134    5.40082396
## 32  -3.40505060  -1.4704228     3.3946318   -0.10762180    1.44494169
## 33  -0.41740574   0.6140688    -3.5738589    0.06285109    0.39340973
## 34  -0.20173830   1.2195569     0.7980935   -0.21294191  568.11732111
## 35   0.61697093  -1.9040947    -1.8336006   -0.60412494    1.24646271
## 36  -0.08920183  27.5242242     0.8960476   -1.39547379  559.94105303
##    a22_a12_upper distanceTu distanceTe distanceTu_lower distanceTu_upper
## 19     1.2113052  1.9255763 0.31600455         1.570796         1.570796
## 20     1.0988574  0.4146835 0.05856812         1.570796         1.570796
## 21     2.7072981  0.2201760 0.12566655         1.570796         1.570796
## 22     1.7135250  0.5957167 0.05061334         1.570796         1.570796
## 23     0.5462526  0.6572633 0.34000744         1.570796         1.570796
## 24     3.8731053  2.5243970 0.64885008         1.570796         1.570796
## 25     2.0934537  0.3528186 1.34001902         1.570796         1.570796
## 26     0.7971894  1.8014160 0.67468953         1.570796         1.570796
## 27     4.0103058  0.3545989 0.82603227         1.570796         1.570796
## 28     1.2836487  1.0480102 0.07682405         1.570796         1.570796
## 29     0.2832304  2.4043384 1.06412693         1.570796         1.570796
## 30     0.5353995  0.4587392 0.34917339         1.570796         1.570796
## 31     1.9955580  0.3890231 0.05806978         1.570796         1.570796
## 32    10.0699110  2.3667470 1.08642471         1.570796         1.570796
## 33     0.8310639  1.2917438 0.34562306         1.570796         1.570796
## 34     1.0160601  1.0976517 0.01458862         1.570796         1.570796
## 35   -13.1558712  0.5165368 0.98504597         1.570796         1.570796
## 36     2.9797918  1.1602615 0.46318556         1.570796         1.570796
##    distanceTe_lower distanceTe_upper distanceTu2 distanceTe2 distanceTu2_lower
## 19         1.570796         1.570796  -1.9255763 -0.31600455         -1.570796
## 20         1.570796         1.570796  -0.4146835 -0.05856812         -1.570796
## 21         1.570796         1.570796  -0.2201760 -0.12566655         -1.570796
## 22         1.570796         1.570796   0.5957167  0.05061334          1.570796
## 23         1.570796         1.570796  -0.6572633 -0.34000744         -1.570796
## 24         1.570796         1.570796  -2.5243970 -0.64885008         -1.570796
## 25         1.570796         1.570796  -0.3528186 -1.34001902         -1.570796
## 26         1.570796         1.570796  -1.8014160 -0.67468953         -1.570796
## 27         1.570796         1.570796  -0.3545989 -0.82603227         -1.570796
## 28         1.570796         1.570796  -1.0480102 -0.07682405          1.570796
## 29         1.570796         1.570796  -2.4043384 -1.06412693         -1.570796
## 30         1.570796         1.570796  -0.4587392 -0.34917339          1.570796
## 31         1.570796         1.570796  -0.3890231 -0.05806978         -1.570796
## 32         1.570796         1.570796  -2.3667470 -1.08642471          1.570796
## 33         1.570796         1.570796  -1.2917438 -0.34562306         -1.570796
## 34         1.570796         1.570796   1.0976517  0.01458862          1.570796
## 35         1.570796         1.570796   0.5165368  0.98504597          1.570796
## 36         1.570796         1.570796  -1.1602615 -0.46318556         -1.570796
##    distanceTe2_lower distanceTu2_upper distanceTe2_upper minDistance
## 19         -1.570796         -1.570796         -1.570796  0.31600455
## 20         -1.570796         -1.570796         -1.570796  0.05856812
## 21         -1.570796         -1.570796         -1.570796  0.12566655
## 22          1.570796          1.570796          1.570796  0.05061334
## 23         -1.570796         -1.570796         -1.570796  0.34000744
## 24         -1.570796         -1.570796         -1.570796  0.64885008
## 25         -1.570796         -1.570796         -1.570796  0.35281858
## 26         -1.570796         -1.570796         -1.570796  0.67468953
## 27         -1.570796         -1.570796         -1.570796  0.35459893
## 28          1.570796          1.570796          1.570796  0.07682405
## 29         -1.570796         -1.570796         -1.570796  1.06412693
## 30          1.570796          1.570796          1.570796  0.34917339
## 31         -1.570796         -1.570796         -1.570796  0.05806978
## 32          1.570796          1.570796          1.570796  1.08642471
## 33         -1.570796         -1.570796         -1.570796  0.34562306
## 34          1.570796          1.570796          1.570796  0.01458862
## 35          1.570796          1.570796          1.570796  0.51653680
## 36         -1.570796         -1.570796         -1.570796  0.46318556
##    minDistance2 minDistance_L minDistance_U minDistance2_lower
## 19  -0.31600455      1.570796      1.570796          -1.570796
## 20  -0.05856812      1.570796      1.570796          -1.570796
## 21  -0.12566655      1.570796      1.570796          -1.570796
## 22   0.05061334      1.570796      1.570796           1.570796
## 23  -0.34000744      1.570796      1.570796          -1.570796
## 24  -0.64885008      1.570796      1.570796          -1.570796
## 25  -0.35281858      1.570796      1.570796          -1.570796
## 26  -0.67468953      1.570796      1.570796          -1.570796
## 27  -0.35459893      1.570796      1.570796          -1.570796
## 28  -0.07682405      1.570796      1.570796          -1.570796
## 29  -1.06412693      1.570796      1.570796          -1.570796
## 30  -0.34917339      1.570796      1.570796          -1.570796
## 31  -0.05806978      1.570796      1.570796          -1.570796
## 32  -1.08642471      1.570796      1.570796          -1.570796
## 33  -0.34562306      1.570796      1.570796          -1.570796
## 34   0.01458862      1.570796      1.570796           1.570796
## 35   0.51653680      1.570796      1.570796           1.570796
## 36  -0.46318556      1.570796      1.570796          -1.570796
##    minDistance2_upper
## 19          -1.570796
## 20          -1.570796
## 21          -1.570796
## 22           1.570796
## 23          -1.570796
## 24          -1.570796
## 25          -1.570796
## 26          -1.570796
## 27          -1.570796
## 28          -1.570796
## 29          -1.570796
## 30          -1.570796
## 31          -1.570796
## 32          -1.570796
## 33          -1.570796
## 34           1.570796
## 35           1.570796
## 36          -1.570796
Stats
# descdist(subset(struct_mat_w0, Environment=="Cd")$distanceTu, discrete = FALSE, boot = 500)
# descdist(subset(struct_mat_w0, Environment=="Cd")$distanceTe , discrete = FALSE, boot = 500)
# 
# descdist(subset(struct_mat_w0, Environment=="N")$distanceTu , discrete = FALSE, boot = 500)
# descdist(subset(struct_mat_w0, Environment=="N")$distanceTe , discrete = FALSE, boot = 500)


dist_Cd_Tu<-glmmTMB(distanceTu~Te_Regime*Tu_Regime, data=subset(struct_mat_w0, Environment=="Cd"), family=Gamma(link="log"))
dist_Cd_Tu2<-glmmTMB(distanceTu~Te_Regime*Tu_Regime, data=subset(struct_mat_w0, Environment=="Cd"), family=Gamma(link="identity"))
dist_Cd_Tu3<-glmmTMB(distanceTu~Te_Regime*Tu_Regime, data=subset(struct_mat_w0, Environment=="Cd"), family=gaussian(link="log"))
#dist_Cd_Tu4<-glmmTMB(distanceTu~Te_Regime*Tu_Regime, data=subset(struct_mat_w0, Environment=="Cd"), family=beta_family(link="log"))

dist_Cd_Te<-glmmTMB(distanceTe~Te_Regime*Tu_Regime, data=subset(struct_mat_w0, Environment=="Cd"), family=Gamma(link="log"))
dist_Cd_Te2<-glmmTMB(distanceTe~Te_Regime*Tu_Regime, data=subset(struct_mat_w0, Environment=="Cd"), family=Gamma(link="identity"))
## Warning in (function (start, objective, gradient = NULL, hessian = NULL, :
## NA/NaN function evaluation
## Warning in (function (start, objective, gradient = NULL, hessian = NULL, :
## NA/NaN function evaluation
## Warning in (function (start, objective, gradient = NULL, hessian = NULL, :
## NA/NaN function evaluation
dist_Cd_Te3<-glmmTMB(distanceTe~Te_Regime*Tu_Regime, data=subset(struct_mat_w0, Environment=="Cd"), family=gaussian(link="log"))
#dist_Cd_Te4<-glmmTMB(distanceTe~Te_Regime*Tu_Regime, data=subset(struct_mat_w0, Environment=="Cd"), family=beta_family(link="logit"))


anova(dist_Cd_Tu, dist_Cd_Tu2, dist_Cd_Tu3)
## Data: subset(struct_mat_w0, Environment == "Cd")
## Models:
## dist_Cd_Tu: distanceTu ~ Te_Regime * Tu_Regime, zi=~0, disp=~1
## dist_Cd_Tu2: distanceTu ~ Te_Regime * Tu_Regime, zi=~0, disp=~1
## dist_Cd_Tu3: distanceTu ~ Te_Regime * Tu_Regime, zi=~0, disp=~1
##             Df    AIC    BIC  logLik deviance Chisq Chi Df Pr(>Chisq)    
## dist_Cd_Tu   5 43.079 47.531 -16.539   33.079                            
## dist_Cd_Tu2  5 43.079 47.531 -16.539   33.079     0      0     <2e-16 ***
## dist_Cd_Tu3  5 49.891 54.343 -19.945   39.891     0      0          1    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
anova(dist_Cd_Te, dist_Cd_Te2, dist_Cd_Te3)
## Data: subset(struct_mat_w0, Environment == "Cd")
## Models:
## dist_Cd_Te: distanceTe ~ Te_Regime * Tu_Regime, zi=~0, disp=~1
## dist_Cd_Te2: distanceTe ~ Te_Regime * Tu_Regime, zi=~0, disp=~1
## dist_Cd_Te3: distanceTe ~ Te_Regime * Tu_Regime, zi=~0, disp=~1
##             Df   AIC    BIC  logLik deviance Chisq Chi Df Pr(>Chisq)    
## dist_Cd_Te   5 18.41 22.861 -4.2047   8.4095                            
## dist_Cd_Te2  5 18.41 22.861 -4.2047   8.4095     0      0     <2e-16 ***
## dist_Cd_Te3  5 26.38 30.832 -8.1899  16.3799     0      0          1    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(dist_Cd_Tu)
##  Family: Gamma  ( log )
## Formula:          distanceTu ~ Te_Regime * Tu_Regime
## Data: subset(struct_mat_w0, Environment == "Cd")
## 
##      AIC      BIC   logLik deviance df.resid 
##     43.1     47.5    -16.5     33.1       13 
## 
## 
## Dispersion estimate for Gamma family (sigma^2): 0.458 
## 
## Conditional model:
##                           Estimate Std. Error z value Pr(>|z|)
## (Intercept)                 0.2824     0.3028   0.933    0.351
## Te_RegimeSR5               -0.5044     0.4282  -1.178    0.239
## Tu_RegimeSR2               -0.3410     0.4542  -0.751    0.453
## Te_RegimeSR5:Tu_RegimeSR2   0.8197     0.6424   1.276    0.202
summary(dist_Cd_Te)
##  Family: Gamma  ( log )
## Formula:          distanceTe ~ Te_Regime * Tu_Regime
## Data: subset(struct_mat_w0, Environment == "Cd")
## 
##      AIC      BIC   logLik deviance df.resid 
##     18.4     22.9     -4.2      8.4       13 
## 
## 
## Dispersion estimate for Gamma family (sigma^2): 0.922 
## 
## Conditional model:
##                           Estimate Std. Error z value Pr(>|z|)
## (Intercept)                -0.3840     0.4293  -0.894    0.371
## Te_RegimeSR5               -0.2533     0.6072  -0.417    0.677
## Tu_RegimeSR2               -0.9097     0.6440  -1.413    0.158
## Te_RegimeSR5:Tu_RegimeSR2   0.6777     0.9108   0.744    0.457
dist_N<-glmmTMB(minDistance~Te_Regime*Tu_Regime, data=subset(struct_mat_w0, Environment=="N"), family=Gamma(link="log"))
dist_Cd<-glmmTMB(minDistance~Te_Regime*Tu_Regime, data=subset(struct_mat_w0, Environment=="Cd"), family=Gamma(link="log"))
summary(dist_Cd)
##  Family: Gamma  ( log )
## Formula:          minDistance ~ Te_Regime * Tu_Regime
## Data: subset(struct_mat_w0, Environment == "Cd")
## 
##      AIC      BIC   logLik deviance df.resid 
##     10.3     14.7     -0.1      0.3       13 
## 
## 
## Dispersion estimate for Gamma family (sigma^2): 0.826 
## 
## Conditional model:
##                           Estimate Std. Error z value Pr(>|z|)  
## (Intercept)                -0.7263     0.4065  -1.787    0.074 .
## Te_RegimeSR5               -0.3504     0.5749  -0.610    0.542  
## Tu_RegimeSR2               -0.5674     0.6097  -0.931    0.352  
## Te_RegimeSR5:Tu_RegimeSR2   0.7748     0.8623   0.898    0.369  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(dist_Cd)
##  Family: Gamma  ( log )
## Formula:          minDistance ~ Te_Regime * Tu_Regime
## Data: subset(struct_mat_w0, Environment == "Cd")
## 
##      AIC      BIC   logLik deviance df.resid 
##     10.3     14.7     -0.1      0.3       13 
## 
## 
## Dispersion estimate for Gamma family (sigma^2): 0.826 
## 
## Conditional model:
##                           Estimate Std. Error z value Pr(>|z|)  
## (Intercept)                -0.7263     0.4065  -1.787    0.074 .
## Te_RegimeSR5               -0.3504     0.5749  -0.610    0.542  
## Tu_RegimeSR2               -0.5674     0.6097  -0.931    0.352  
## Te_RegimeSR5:Tu_RegimeSR2   0.7748     0.8623   0.898    0.369  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(dist_N)
##  Family: Gamma  ( log )
## Formula:          minDistance ~ Te_Regime * Tu_Regime
## Data: subset(struct_mat_w0, Environment == "N")
## 
##      AIC      BIC   logLik deviance df.resid 
##     -6.8     -2.4      8.4    -16.8       13 
## 
## 
## Dispersion estimate for Gamma family (sigma^2): 0.535 
## 
## Conditional model:
##                           Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                -1.4440     0.3272  -4.413 1.02e-05 ***
## Te_RegimeSR5                0.2572     0.4628   0.556    0.578    
## Tu_RegimeSR2                0.1428     0.4908   0.291    0.771    
## Te_RegimeSR5:Tu_RegimeSR2  -0.5336     0.6942  -0.769    0.442    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
dist_glm<-glmmTMB(minDistance~Te_Regime*Tu_Regime*Environment, data=struct_mat_w0, family=Gamma(link="log"))
summary(dist_glm)
##  Family: Gamma  ( log )
## Formula:          minDistance ~ Te_Regime * Tu_Regime * Environment
## Data: struct_mat_w0
## 
##      AIC      BIC   logLik deviance df.resid 
##      2.5     16.7      7.8    -15.5       27 
## 
## 
## Dispersion estimate for Gamma family (sigma^2): 0.683 
## 
## Conditional model:
##                                        Estimate Std. Error z value Pr(>|z|)  
## (Intercept)                             -0.7263     0.3696  -1.965   0.0494 *
## Te_RegimeSR5                            -0.3504     0.5227  -0.670   0.5027  
## Tu_RegimeSR2                            -0.5674     0.5544  -1.023   0.3061  
## EnvironmentN                            -0.7178     0.5227  -1.373   0.1697  
## Te_RegimeSR5:Tu_RegimeSR2                0.7748     0.7841   0.988   0.3231  
## Te_RegimeSR5:EnvironmentN                0.6076     0.7393   0.822   0.4112  
## Tu_RegimeSR2:EnvironmentN                0.7102     0.7841   0.906   0.3650  
## Te_RegimeSR5:Tu_RegimeSR2:EnvironmentN  -1.3084     1.1089  -1.180   0.2380  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
dist_glm2<-glmmTMB(minDistance~Te_Regime+Tu_Regime+Environment, data=struct_mat_w0, family=Gamma(link="log"))
dist_glm3<-glmmTMB(minDistance~Te_Regime*Environment+Tu_Regime*Environment, data=struct_mat_w0, family=Gamma(link="log"))
summary(dist_glm3)
##  Family: Gamma  ( log )
## Formula:          
## minDistance ~ Te_Regime * Environment + Tu_Regime * Environment
## Data: struct_mat_w0
## 
##      AIC      BIC   logLik deviance df.resid 
##     -0.1     11.0      7.1    -14.1       29 
## 
## 
## Dispersion estimate for Gamma family (sigma^2): 0.706 
## 
## Conditional model:
##                            Estimate Std. Error z value Pr(>|z|)   
## (Intercept)               -0.883241   0.313953  -2.813   0.0049 **
## Te_RegimeSR5              -0.007078   0.403306  -0.018   0.9860   
## EnvironmentN              -0.435413   0.467933  -0.930   0.3521   
## Tu_RegimeSR2              -0.171602   0.405819  -0.423   0.6724   
## Te_RegimeSR5:EnvironmentN  0.027484   0.567633   0.048   0.9614   
## EnvironmentN:Tu_RegimeSR2  0.051585   0.571169   0.090   0.9280   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Anova(dist_glm2)
## Analysis of Deviance Table (Type II Wald chisquare tests)
## 
## Response: minDistance
##              Chisq Df Pr(>Chisq)
## Te_Regime   0.0001  1     0.9926
## Tu_Regime   0.2752  1     0.5999
## Environment 2.0271  1     0.1545
anova(dist_glm, dist_glm2, dist_glm3)
## Data: struct_mat_w0
## Models:
## dist_glm2: minDistance ~ Te_Regime + Tu_Regime + Environment, zi=~0, disp=~1
## dist_glm3: minDistance ~ Te_Regime * Environment + Tu_Regime * Environment, zi=~0, disp=~1
## dist_glm: minDistance ~ Te_Regime * Tu_Regime * Environment, zi=~0, disp=~1
##           Df     AIC     BIC logLik deviance  Chisq Chi Df Pr(>Chisq)
## dist_glm2  5 -4.1109  3.8067 7.0554  -14.111                         
## dist_glm3  7 -0.1216 10.9630 7.0608  -14.122 0.0108      2     0.9946
## dist_glm   9  2.4695 16.7212 7.7652  -15.530 1.4088      2     0.4944
dist_Cd_Te<-glmmTMB(distanceTe~Environment, data=struct_mat_w0, family=Gamma(link="log"))
summary(dist_Cd_Te)
##  Family: Gamma  ( log )
## Formula:          distanceTe ~ Environment
## Data: struct_mat_w0
## 
##      AIC      BIC   logLik deviance df.resid 
##     25.2     30.0     -9.6     19.2       33 
## 
## 
## Dispersion estimate for Gamma family (sigma^2): 0.662 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  -0.71295    0.19173  -3.719   0.0002 ***
## EnvironmentN  0.05222    0.27115   0.193   0.8473    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
dist_Cd_Tu<-glmmTMB(distanceTu~Environment, data=struct_mat_w0, family=Gamma(link="log"))
summary(dist_Cd_Tu)
##  Family: Gamma  ( log )
## Formula:          distanceTu ~ Environment
## Data: struct_mat_w0
## 
##      AIC      BIC   logLik deviance df.resid 
##     75.6     80.4    -34.8     69.6       33 
## 
## 
## Dispersion estimate for Gamma family (sigma^2): 0.962 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)
## (Intercept)   0.08412    0.23122   0.364    0.716
## EnvironmentN -0.23322    0.32700  -0.713    0.476
dist_Cd<-glmmTMB(minDistance~Environment, data=struct_mat_w0, family=Gamma(link="log"))
summary(dist_Cd)
##  Family: Gamma  ( log )
## Formula:          minDistance ~ Environment
## Data: struct_mat_w0
## 
##      AIC      BIC   logLik deviance df.resid 
##     -7.8     -3.1      6.9    -13.8       33 
## 
## 
## Dispersion estimate for Gamma family (sigma^2): 0.71 
## 
## Conditional model:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)   -0.9594     0.1986  -4.830 1.36e-06 ***
## EnvironmentN  -0.4005     0.2809  -1.426    0.154    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

4 - Can we predict the outcome of species interactions?

str(sum_coex_g42_res2)
## 'data.frame':    1440 obs. of  10 variables:
##  $ Rep2     : Factor w/ 5 levels "1","2","3","4",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ SRTu     : Factor w/ 2 levels "Tu1","Tu2": 1 1 1 1 1 1 1 1 1 1 ...
##  $ SRTe     : Factor w/ 2 levels "Te4","Te5": 1 1 1 1 1 1 1 1 1 1 ...
##  $ Box2     : Factor w/ 10 levels "1","2","3","4",..: 1 1 1 1 1 1 1 1 2 2 ...
##  $ Leaf2    : chr  "2" "2" "3" "3" ...
##  $ X1st.pair: Factor w/ 8 levels "2.4","24c","2c4",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ X2nd.pair: Factor w/ 10 levels "1.4","2.4","24c",..: 5 5 5 5 5 5 5 5 5 5 ...
##  $ Env      : chr  "Cd" "water" "Cd" "water" ...
##  $ av_Te    : int  85 0 90 0 18 6 206 116 9 2 ...
##  $ av_Tu    : int  11 1 2 1 0 7 22 33 0 3 ...
coex_no_het<-subset(sum_coex_g42_res2, Env!="Heterogeneous")

coex_no_het2<-coex_no_het %>%
  group_by(SRTu, SRTe, Rep2, Box2, Env) %>%
  summarize(sumTe=sum(av_Te, na.rm=TRUE), sumTu=sum(av_Tu, na.rm=TRUE)) %>% as.data.frame()
## `summarise()` has grouped output by 'SRTu', 'SRTe', 'Rep2', 'Box2'. You can
## override using the `.groups` argument.
coex_no_het2$Te_ratio<-coex_no_het2$sumTe/(coex_no_het2$sumTe+coex_no_het2$sumTu)

coex_no_het2$Te_ratio[which(coex_no_het2$Te_ratio=="NaN")]<-0

coex_no_het2$Tu_Regime<-mapvalues(coex_no_het2$SRTu, c("Tu2", "Tu1"), c("SR2", "SR1"))

coex_no_het2$Te_Regime<-mapvalues(coex_no_het2$SRTe, c("Te4", "Te5"), c("SR4", "SR5"))

Predicting once

pred_coex_RK_REP<-expand_grid(Te=c("SR4","SR5"), Tu=c("SR1", "SR2"), Environment= c("N", "Cd"))

pred_coex_RK_REP$predTu1<-sapply(c(1:length(pred_coex_RK_REP$Tu)), function(x){
  aux_alphas<-subset(param_all_REP, Tu_Regime==as.character(pred_coex_RK_REP$Tu[x]) & Te_Regime==as.character(pred_coex_RK_REP$Te[x]) & Environment==as.character(pred_coex_RK_REP$Environment[x]))

  bl<-aux_alphas$Tu_lambda[1]*6* exp(-aux_alphas$Tu_intra[1]*6 - aux_alphas$Tu_inter[1]*6)
  
  bl
  })

pred_coex_RK_REP$predTe1<-sapply(c(1:length(pred_coex_RK_REP$Te)), function(x){
  aux_alphas<-subset(param_all_REP, Tu_Regime==as.character(pred_coex_RK_REP$Tu[x]) & Te_Regime==as.character(pred_coex_RK_REP$Te[x]) & Environment==as.character(pred_coex_RK_REP$Environment[x]))

  bl<-aux_alphas$Te_lambda[1]*6* exp(-aux_alphas$Te_intra[1]*6 - aux_alphas$Te_inter[1]*6)
  
  bl
  })


pred_coex_RK_REP$predTu2<-sapply(c(1:length(pred_coex_RK_REP$Tu)), function(x){
  aux_alphas<-subset(param_all_REP, Tu_Regime==as.character(pred_coex_RK_REP$Tu[x]) & Te_Regime==as.character(pred_coex_RK_REP$Te[x]) & Environment==as.character(pred_coex_RK_REP$Environment[x]))

  bl<-aux_alphas$Tu_lambda[1]*pred_coex_RK_REP$predTu1[x]* exp(-aux_alphas$Tu_intra[1]*pred_coex_RK_REP$predTu1[x]- aux_alphas$Tu_inter[1]*pred_coex_RK_REP$predTe1[x])
  
  bl
  })

pred_coex_RK_REP$predTe2<-sapply(c(1:length(pred_coex_RK_REP$Te)), function(x){
  aux_alphas<-subset(param_all_REP, Tu_Regime==as.character(pred_coex_RK_REP$Tu[x]) & Te_Regime==as.character(pred_coex_RK_REP$Te[x]) & Environment==as.character(pred_coex_RK_REP$Environment[x]))

  bl<-aux_alphas$Te_lambda[1]*pred_coex_RK_REP$predTe1[x]* exp(-aux_alphas$Te_intra[1]*pred_coex_RK_REP$predTe1[x] - aux_alphas$Te_inter[1]*pred_coex_RK_REP$predTu1[x])
  
  bl
  })

x<-1
# lower - stronger alpha and lower lambda
pred_coex_RK_REP$predTu1_L<-sapply(c(1:length(pred_coex_RK_REP$Tu)), function(x){
  aux_alphas<-subset(param_all_REP_lower, Tu_Regime==as.character(pred_coex_RK_REP$Tu[x]) & Te_Regime==as.character(pred_coex_RK_REP$Te[x]) & Environment==as.character(pred_coex_RK_REP$Environment[x]))
  aux_lambda<-subset(param_all_REP_lower, Tu_Regime==as.character(pred_coex_RK_REP$Tu[x]) & Te_Regime==as.character(pred_coex_RK_REP$Te[x]) & Environment==as.character(pred_coex_RK_REP$Environment[x]))

  bl<-aux_lambda$Tu_lambda[1]*6* exp(-aux_alphas$Tu_intra[1]*6- aux_alphas$Tu_inter[1]*6)
  
  bl
  })

pred_coex_RK_REP$predTe1_L<-sapply(c(1:length(pred_coex_RK_REP$Te)), function(x){
  aux_alphas<-subset(param_all_REP_lower, Tu_Regime==as.character(pred_coex_RK_REP$Tu[x]) & Te_Regime==as.character(pred_coex_RK_REP$Te[x]) & Environment==as.character(pred_coex_RK_REP$Environment[x]))
  aux_lambda<-subset(param_all_REP_lower, Tu_Regime==as.character(pred_coex_RK_REP$Tu[x]) & Te_Regime==as.character(pred_coex_RK_REP$Te[x]) & Environment==as.character(pred_coex_RK_REP$Environment[x]))

  bl<-aux_lambda$Te_lambda[1]*6* exp(-aux_alphas$Te_intra[1]*6 - aux_alphas$Te_inter[1]*6)
  
  bl
  })


pred_coex_RK_REP$predTu2_L<-sapply(c(1:length(pred_coex_RK_REP$Tu)), function(x){
    aux_alphas<-subset(param_all_REP_lower, Tu_Regime==as.character(pred_coex_RK_REP$Tu[x]) & Te_Regime==as.character(pred_coex_RK_REP$Te[x]) & Environment==as.character(pred_coex_RK_REP$Environment[x]))
  aux_lambda<-subset(param_all_REP_lower, Tu_Regime==as.character(pred_coex_RK_REP$Tu[x]) & Te_Regime==as.character(pred_coex_RK_REP$Te[x]) & Environment==as.character(pred_coex_RK_REP$Environment[x]))

  bl<-aux_lambda$Tu_lambda[1]*pred_coex_RK_REP$predTu1_L[x]* exp(-aux_alphas$Tu_intra[1]*pred_coex_RK_REP$predTu1_L[x]- aux_alphas$Tu_inter[1]*pred_coex_RK_REP$predTe1_L[x])
  
  bl
  })

pred_coex_RK_REP$predTe2_L<-sapply(c(1:length(pred_coex_RK_REP$Te)), function(x){
    aux_alphas<-subset(param_all_REP_lower, Tu_Regime==as.character(pred_coex_RK_REP$Tu[x]) & Te_Regime==as.character(pred_coex_RK_REP$Te[x]) & Environment==as.character(pred_coex_RK_REP$Environment[x]))
  aux_lambda<-subset(param_all_REP_lower, Tu_Regime==as.character(pred_coex_RK_REP$Tu[x]) & Te_Regime==as.character(pred_coex_RK_REP$Te[x]) & Environment==as.character(pred_coex_RK_REP$Environment[x]))

  bl<-aux_lambda$Te_lambda[1]*pred_coex_RK_REP$predTe1_L[x]* exp(-aux_alphas$Te_intra[1]*pred_coex_RK_REP$predTe1_L[x] - aux_alphas$Te_inter[1]*pred_coex_RK_REP$predTu1_L[x])
  
  bl
  })

# upper
pred_coex_RK_REP$predTu1_U<-sapply(c(1:length(pred_coex_RK_REP$Tu)), function(x){
  aux_alphas<-subset(param_all_REP_upper, Tu_Regime==as.character(pred_coex_RK_REP$Tu[x]) & Te_Regime==as.character(pred_coex_RK_REP$Te[x]) & Environment==as.character(pred_coex_RK_REP$Environment[x]))
  aux_lambda<-subset(param_all_REP_upper, Tu_Regime==as.character(pred_coex_RK_REP$Tu[x]) & Te_Regime==as.character(pred_coex_RK_REP$Te[x]) & Environment==as.character(pred_coex_RK_REP$Environment[x]))

  bl<-aux_lambda$Tu_lambda[1]*6* exp(-aux_alphas$Tu_intra[1]*6- aux_alphas$Tu_inter[1]*6)
  
  bl
  })

pred_coex_RK_REP$predTe1_U<-sapply(c(1:length(pred_coex_RK_REP$Te)), function(x){
  aux_alphas<-subset(param_all_REP_upper, Tu_Regime==as.character(pred_coex_RK_REP$Tu[x]) & Te_Regime==as.character(pred_coex_RK_REP$Te[x]) & Environment==as.character(pred_coex_RK_REP$Environment[x]))
  aux_lambda<-subset(param_all_REP_upper, Tu_Regime==as.character(pred_coex_RK_REP$Tu[x]) & Te_Regime==as.character(pred_coex_RK_REP$Te[x]) & Environment==as.character(pred_coex_RK_REP$Environment[x]))

  bl<-aux_lambda$Te_lambda[1]*6* exp(-aux_alphas$Te_intra[1]*6 - aux_alphas$Te_inter[1]*6)
  
  bl
  })


pred_coex_RK_REP$predTu2_U<-sapply(c(1:length(pred_coex_RK_REP$Tu)), function(x){
  aux_alphas<-subset(param_all_REP_upper, Tu_Regime==as.character(pred_coex_RK_REP$Tu[x]) & Te_Regime==as.character(pred_coex_RK_REP$Te[x]) & Environment==as.character(pred_coex_RK_REP$Environment[x]))
  aux_lambda<-subset(param_all_REP_upper, Tu_Regime==as.character(pred_coex_RK_REP$Tu[x]) & Te_Regime==as.character(pred_coex_RK_REP$Te[x]) & Environment==as.character(pred_coex_RK_REP$Environment[x]))

  bl<-aux_lambda$Tu_lambda[1]* pred_coex_RK_REP$predTu1_U[x]* exp(-aux_alphas$Tu_intra[1]*pred_coex_RK_REP$predTu1_U[x]- aux_alphas$Tu_inter[1]*pred_coex_RK_REP$predTe1_U[x])
  
  bl
  })

pred_coex_RK_REP$predTe2_U<-sapply(c(1:length(pred_coex_RK_REP$Te)), function(x){
 aux_alphas<-subset(param_all_REP_upper, Tu_Regime==as.character(pred_coex_RK_REP$Tu[x]) & Te_Regime==as.character(pred_coex_RK_REP$Te[x]) & Environment==as.character(pred_coex_RK_REP$Environment[x]))
  aux_lambda<-subset(param_all_REP_upper, Tu_Regime==as.character(pred_coex_RK_REP$Tu[x]) & Te_Regime==as.character(pred_coex_RK_REP$Te[x]) & Environment==as.character(pred_coex_RK_REP$Environment[x]))

  bl<-aux_lambda$Te_lambda[1]*pred_coex_RK_REP$predTe1_U[x]* exp(-aux_alphas$Te_intra[1]*pred_coex_RK_REP$predTe1_U[x] - aux_alphas$Te_inter[1]*pred_coex_RK_REP$predTu1_U[x])
  
  bl
  })


names(pred_coex_RK_REP)[1:3]<-c("SRTe", "SRTu", "Env")

pred_coex_RK_REP<-as.data.frame(pred_coex_RK_REP)

Predicting per replicate

pred_coex_RK_w0<-as.data.frame(expand_grid(Te=c("SR4","SR5"), Tu=c("SR1", "SR2"), Environment= c("N", "Cd"), Replicate=c(1,2,3,4,5)))

pred_coex_RK_w0<- pred_coex_RK_w0[- which(pred_coex_RK_w0$Replicate==2 & pred_coex_RK_w0$Tu=="SR2" & pred_coex_RK_w0$Environment=="Cd"),]


pred_coex_RK_w0$predTu1<-sapply(c(1:length(pred_coex_RK_w0$Tu)), function(x){
  aux_alphas<-subset(param_all_w0, Tu_Regime==as.character(pred_coex_RK_w0$Tu[x]) & Te_Regime==as.character(pred_coex_RK_w0$Te[x]) & Environment==as.character(pred_coex_RK_w0$Environment[x]) & Replicate==pred_coex_RK_w0$Replicate[x])

  bl<-aux_alphas$Tu_lambda[1]*6* exp(-aux_alphas$Tu_intra[1]*6 - aux_alphas$Tu_inter[1]*6)
  
  bl
  })

pred_coex_RK_w0$predTe1<-sapply(c(1:length(pred_coex_RK_w0$Te)), function(x){
  aux_alphas<-subset(param_all_w0, Tu_Regime==as.character(pred_coex_RK_w0$Tu[x]) & Te_Regime==as.character(pred_coex_RK_w0$Te[x]) & Environment==as.character(pred_coex_RK_w0$Environment[x]) & Replicate==pred_coex_RK_w0$Replicate[x])

  bl<-aux_alphas$Te_lambda[1]*6* exp(-aux_alphas$Te_intra[1]*6 - aux_alphas$Te_inter[1]*6)
  
  bl
  })


pred_coex_RK_w0$predTu2<-sapply(c(1:length(pred_coex_RK_w0$Tu)), function(x){
  aux_alphas<-subset(param_all_w0, Tu_Regime==as.character(pred_coex_RK_w0$Tu[x]) & Te_Regime==as.character(pred_coex_RK_w0$Te[x]) & Environment==as.character(pred_coex_RK_w0$Environment[x]) & Replicate==pred_coex_RK_w0$Replicate[x])

  bl<-aux_alphas$Tu_lambda[1]*pred_coex_RK_w0$predTu1[x]* exp(-aux_alphas$Tu_intra[1]*pred_coex_RK_w0$predTu1[x]- aux_alphas$Tu_inter[1]*pred_coex_RK_w0$predTe1[x])
  
  bl
  })

pred_coex_RK_w0$predTe2<-sapply(c(1:length(pred_coex_RK_w0$Te)), function(x){
  aux_alphas<-subset(param_all_w0, Tu_Regime==as.character(pred_coex_RK_w0$Tu[x]) & Te_Regime==as.character(pred_coex_RK_w0$Te[x]) & Environment==as.character(pred_coex_RK_w0$Environment[x]) & Replicate==pred_coex_RK_w0$Replicate[x])

  bl<-aux_alphas$Te_lambda[1]*pred_coex_RK_w0$predTe1[x]* exp(-aux_alphas$Te_intra[1]*pred_coex_RK_w0$predTe1[x] - aux_alphas$Te_inter[1]*pred_coex_RK_w0$predTu1[x])
  
  bl
  })

x<-1
# lower - stronger alpha and lower lambda
pred_coex_RK_w0$predTu1_L<-sapply(c(1:length(pred_coex_RK_w0$Tu)), function(x){
  aux_alphas<-subset(param_all_w0_upper, Tu_Regime==as.character(pred_coex_RK_w0$Tu[x]) & Te_Regime==as.character(pred_coex_RK_w0$Te[x]) & Environment==as.character(pred_coex_RK_w0$Environment[x]) & Replicate==pred_coex_RK_w0$Replicate[x])
  aux_lambda<-subset(param_all_w0_lower, Tu_Regime==as.character(pred_coex_RK_w0$Tu[x]) & Te_Regime==as.character(pred_coex_RK_w0$Te[x]) & Environment==as.character(pred_coex_RK_w0$Environment[x]) & Replicate==pred_coex_RK_w0$Replicate[x])

  bl<-aux_lambda$Tu_lambda[1]*6* exp(-aux_alphas$Tu_intra[1]*6- aux_alphas$Tu_inter[1]*6)
  
  bl
  })

pred_coex_RK_w0$predTe1_L<-sapply(c(1:length(pred_coex_RK_w0$Te)), function(x){
  aux_alphas<-subset(param_all_w0_upper, Tu_Regime==as.character(pred_coex_RK_w0$Tu[x]) & Te_Regime==as.character(pred_coex_RK_w0$Te[x]) & Environment==as.character(pred_coex_RK_w0$Environment[x]) & Replicate==pred_coex_RK_w0$Replicate[x])
  aux_lambda<-subset(param_all_w0_lower, Tu_Regime==as.character(pred_coex_RK_w0$Tu[x]) & Te_Regime==as.character(pred_coex_RK_w0$Te[x]) & Environment==as.character(pred_coex_RK_w0$Environment[x]) & Replicate==pred_coex_RK_w0$Replicate[x])

  bl<-aux_lambda$Te_lambda[1]*6* exp(-aux_alphas$Te_intra[1]*6 - aux_alphas$Te_inter[1]*6)
  
  bl
  })


pred_coex_RK_w0$predTu2_L<-sapply(c(1:length(pred_coex_RK_w0$Tu)), function(x){
    aux_alphas<-subset(param_all_w0_upper, Tu_Regime==as.character(pred_coex_RK_w0$Tu[x]) & Te_Regime==as.character(pred_coex_RK_w0$Te[x]) & Environment==as.character(pred_coex_RK_w0$Environment[x]) & Replicate==pred_coex_RK_w0$Replicate[x])
  aux_lambda<-subset(param_all_w0_lower, Tu_Regime==as.character(pred_coex_RK_w0$Tu[x]) & Te_Regime==as.character(pred_coex_RK_w0$Te[x]) & Environment==as.character(pred_coex_RK_w0$Environment[x]) & Replicate==pred_coex_RK_w0$Replicate[x])

  bl<-aux_lambda$Tu_lambda[1]*pred_coex_RK_w0$predTu1_L[x]* exp(-aux_alphas$Tu_intra[1]*pred_coex_RK_w0$predTu1_L[x]- aux_alphas$Tu_inter[1]*pred_coex_RK_w0$predTe1_L[x])
  
  bl
  })

pred_coex_RK_w0$predTe2_L<-sapply(c(1:length(pred_coex_RK_w0$Te)), function(x){
    aux_alphas<-subset(param_all_w0_upper, Tu_Regime==as.character(pred_coex_RK_w0$Tu[x]) & Te_Regime==as.character(pred_coex_RK_w0$Te[x]) & Environment==as.character(pred_coex_RK_w0$Environment[x]) & Replicate==pred_coex_RK_w0$Replicate[x])
  aux_lambda<-subset(param_all_w0_lower, Tu_Regime==as.character(pred_coex_RK_w0$Tu[x]) & Te_Regime==as.character(pred_coex_RK_w0$Te[x]) & Environment==as.character(pred_coex_RK_w0$Environment[x]) & Replicate==pred_coex_RK_w0$Replicate[x])

  bl<-aux_lambda$Te_lambda[1]*pred_coex_RK_w0$predTe1_L[x]* exp(-aux_alphas$Te_intra[1]*pred_coex_RK_w0$predTe1_L[x] - aux_alphas$Te_inter[1]*pred_coex_RK_w0$predTu1_L[x])
  
  bl
  })

# upper
pred_coex_RK_w0$predTu1_U<-sapply(c(1:length(pred_coex_RK_w0$Tu)), function(x){
  aux_alphas<-subset(param_all_w0_lower, Tu_Regime==as.character(pred_coex_RK_w0$Tu[x]) & Te_Regime==as.character(pred_coex_RK_w0$Te[x]) & Environment==as.character(pred_coex_RK_w0$Environment[x]) & Replicate==pred_coex_RK_w0$Replicate[x])
  aux_lambda<-subset(param_all_w0_upper, Tu_Regime==as.character(pred_coex_RK_w0$Tu[x]) & Te_Regime==as.character(pred_coex_RK_w0$Te[x]) & Environment==as.character(pred_coex_RK_w0$Environment[x]) & Replicate==pred_coex_RK_w0$Replicate[x])

  bl<-aux_lambda$Tu_lambda[1]*6* exp(-aux_alphas$Tu_intra[1]*6- aux_alphas$Tu_inter[1]*6)
  
  bl
  })

pred_coex_RK_w0$predTe1_U<-sapply(c(1:length(pred_coex_RK_w0$Te)), function(x){
  aux_alphas<-subset(param_all_w0_lower, Tu_Regime==as.character(pred_coex_RK_w0$Tu[x]) & Te_Regime==as.character(pred_coex_RK_w0$Te[x]) & Environment==as.character(pred_coex_RK_w0$Environment[x]) & Replicate==pred_coex_RK_w0$Replicate[x])
  aux_lambda<-subset(param_all_w0_upper, Tu_Regime==as.character(pred_coex_RK_w0$Tu[x]) & Te_Regime==as.character(pred_coex_RK_w0$Te[x]) & Environment==as.character(pred_coex_RK_w0$Environment[x]) & Replicate==pred_coex_RK_w0$Replicate[x])

  bl<-aux_lambda$Te_lambda[1]*6* exp(-aux_alphas$Te_intra[1]*6 - aux_alphas$Te_inter[1]*6)
  
  bl
  })


pred_coex_RK_w0$predTu2_U<-sapply(c(1:length(pred_coex_RK_w0$Tu)), function(x){
  aux_alphas<-subset(param_all_w0_lower, Tu_Regime==as.character(pred_coex_RK_w0$Tu[x]) & Te_Regime==as.character(pred_coex_RK_w0$Te[x]) & Environment==as.character(pred_coex_RK_w0$Environment[x]) & Replicate==pred_coex_RK_w0$Replicate[x])
  aux_lambda<-subset(param_all_w0_upper, Tu_Regime==as.character(pred_coex_RK_w0$Tu[x]) & Te_Regime==as.character(pred_coex_RK_w0$Te[x]) & Environment==as.character(pred_coex_RK_w0$Environment[x]) & Replicate==pred_coex_RK_w0$Replicate[x])

  bl<-aux_lambda$Tu_lambda[1]* pred_coex_RK_w0$predTu1_U[x]* exp(-aux_alphas$Tu_intra[1]*pred_coex_RK_w0$predTu1_U[x]- aux_alphas$Tu_inter[1]*pred_coex_RK_w0$predTe1_U[x])
  
  bl
  })

pred_coex_RK_w0$predTe2_U<-sapply(c(1:length(pred_coex_RK_w0$Te)), function(x){
 aux_alphas<-subset(param_all_w0_lower, Tu_Regime==as.character(pred_coex_RK_w0$Tu[x]) & Te_Regime==as.character(pred_coex_RK_w0$Te[x]) & Environment==as.character(pred_coex_RK_w0$Environment[x]) & Replicate==pred_coex_RK_w0$Replicate[x])
  aux_lambda<-subset(param_all_w0_upper, Tu_Regime==as.character(pred_coex_RK_w0$Tu[x]) & Te_Regime==as.character(pred_coex_RK_w0$Te[x]) & Environment==as.character(pred_coex_RK_w0$Environment[x]) & Replicate==pred_coex_RK_w0$Replicate[x])

  bl<-aux_lambda$Te_lambda[1]*pred_coex_RK_w0$predTe1_U[x]* exp(-aux_alphas$Te_intra[1]*pred_coex_RK_w0$predTe1_U[x] - aux_alphas$Te_inter[1]*pred_coex_RK_w0$predTu1_U[x])
  
  bl
  })


names(pred_coex_RK_w0)[1:3]<-c("SRTe", "SRTu", "Env")

pred_coex_RK_w0<-as.data.frame(pred_coex_RK_w0)

Empirical

coex_g42_rep
##      Rep2 Leaf2 SRTu SRTe   Env Box2 sum_Te sum_Tu
## 1       1     2  Tu1  Te4    Cd    1     85     11
## 2       1     2  Tu1  Te4    Cd    2      9      0
## 3       1     2  Tu1  Te4    Cd    3      0      0
## 4       1     2  Tu1  Te4    Cd    4     66      0
## 5       1     2  Tu1  Te4    Cd    5     35      0
## 6       1     2  Tu1  Te4    Cd    6    164     28
## 7       1     2  Tu1  Te4    Cd    7     29      2
## 8       1     2  Tu1  Te4    Cd    8     48      2
## 9       1     2  Tu1  Te4    Cd    9      0      0
## 10      1     2  Tu1  Te4    Cd   10     22      0
## 11      1     2  Tu1  Te4 water    1      0      1
## 12      1     2  Tu1  Te4 water    2      2      3
## 13      1     2  Tu1  Te4 water    3     18      8
## 14      1     2  Tu1  Te4 water    4     30      9
## 15      1     2  Tu1  Te4 water    5      7      8
## 16      1     2  Tu1  Te4 water    6     23      8
## 17      1     2  Tu1  Te4 water    7     35     30
## 18      1     2  Tu1  Te4 water    8     18     35
## 19      1     2  Tu1  Te4 water    9     19     12
## 20      1     2  Tu1  Te4 water   10     28     77
## 21      1     2  Tu1  Te5    Cd    1      7      4
## 22      1     2  Tu1  Te5    Cd    2     39      2
## 23      1     2  Tu1  Te5    Cd    3     31      2
## 24      1     2  Tu1  Te5    Cd    4      7      0
## 25      1     2  Tu1  Te5    Cd    5     89      2
## 26      1     2  Tu1  Te5    Cd    6     48      0
## 27      1     2  Tu1  Te5    Cd    7     18      0
## 28      1     2  Tu1  Te5    Cd    8     51      0
## 29      1     2  Tu1  Te5    Cd    9     11      0
## 30      1     2  Tu1  Te5    Cd   10     21      0
## 31      1     2  Tu1  Te5 water    1      0      0
## 32      1     2  Tu1  Te5 water    2      0      0
## 33      1     2  Tu1  Te5 water    3      0      0
## 34      1     2  Tu1  Te5 water    4      0      1
## 35      1     2  Tu1  Te5 water    5      0      0
## 36      1     2  Tu1  Te5 water    6     39      4
## 37      1     2  Tu1  Te5 water    7     85      5
## 38      1     2  Tu1  Te5 water    8     34     39
## 39      1     2  Tu1  Te5 water    9     52     16
## 40      1     2  Tu1  Te5 water   10      2      2
## 41      1     2  Tu2  Te4    Cd    1    134     19
## 42      1     2  Tu2  Te4    Cd    2      6      0
## 43      1     2  Tu2  Te4    Cd    3      6      1
## 44      1     2  Tu2  Te4    Cd    4      0      0
## 45      1     2  Tu2  Te4    Cd    5      0      0
## 46      1     2  Tu2  Te4    Cd    6      7      1
## 47      1     2  Tu2  Te4    Cd    7     12      0
## 48      1     2  Tu2  Te4    Cd    8      1      0
## 49      1     2  Tu2  Te4    Cd    9      9      0
## 50      1     2  Tu2  Te4    Cd   10      5      0
## 51      1     2  Tu2  Te4 water    1      0      0
## 52      1     2  Tu2  Te4 water    2      0      0
## 53      1     2  Tu2  Te4 water    3      0      0
## 54      1     2  Tu2  Te4 water    4      0      0
## 55      1     2  Tu2  Te4 water    5      0      0
## 56      1     2  Tu2  Te4 water    6      0      3
## 57      1     2  Tu2  Te4 water    7     31      8
## 58      1     2  Tu2  Te4 water    8     50      3
## 59      1     2  Tu2  Te4 water    9     94      1
## 60      1     2  Tu2  Te4 water   10     62      1
## 61      1     2  Tu2  Te5    Cd    1     39      7
## 62      1     2  Tu2  Te5    Cd    2     40      2
## 63      1     2  Tu2  Te5    Cd    3      2      0
## 64      1     2  Tu2  Te5    Cd    4     19      0
## 65      1     2  Tu2  Te5    Cd    5     14     11
## 66      1     2  Tu2  Te5    Cd    6      8      0
## 67      1     2  Tu2  Te5    Cd    7      0      0
## 68      1     2  Tu2  Te5    Cd    8      2      2
## 69      1     2  Tu2  Te5    Cd    9      1      1
## 70      1     2  Tu2  Te5    Cd   10     16      0
## 71      1     2  Tu2  Te5 water    1      1      1
## 72      1     2  Tu2  Te5 water    2      0      0
## 73      1     2  Tu2  Te5 water    3      0      0
## 74      1     2  Tu2  Te5 water    4      0      0
## 75      1     2  Tu2  Te5 water    5      0      0
## 76      1     2  Tu2  Te5 water    6     48      0
## 77      1     2  Tu2  Te5 water    7    111     40
## 78      1     2  Tu2  Te5 water    8      0      0
## 79      1     2  Tu2  Te5 water    9    191     41
## 80      1     2  Tu2  Te5 water   10      3      0
## 81      1     3  Tu1  Te4    Cd    1     90      2
## 82      1     3  Tu1  Te4    Cd    2      0      0
## 83      1     3  Tu1  Te4    Cd    3      0      0
## 84      1     3  Tu1  Te4    Cd    4      0      0
## 85      1     3  Tu1  Te4    Cd    5     12      2
## 86      1     3  Tu1  Te4    Cd    6     55     12
## 87      1     3  Tu1  Te4    Cd    7     20      0
## 88      1     3  Tu1  Te4    Cd    8     13      0
## 89      1     3  Tu1  Te4    Cd    9     18      0
## 90      1     3  Tu1  Te4    Cd   10      5      0
## 91      1     3  Tu1  Te4 water    1      0      1
## 92      1     3  Tu1  Te4 water    2      9      3
## 93      1     3  Tu1  Te4 water    3      6      1
## 94      1     3  Tu1  Te4 water    4      8      8
## 95      1     3  Tu1  Te4 water    5      3      6
## 96      1     3  Tu1  Te4 water    6      0      0
## 97      1     3  Tu1  Te4 water    7     19      6
## 98      1     3  Tu1  Te4 water    8      0      0
## 99      1     3  Tu1  Te4 water    9      0      0
## 100     1     3  Tu1  Te4 water   10      0      1
## 101     1     3  Tu1  Te5    Cd    1     32      1
## 102     1     3  Tu1  Te5    Cd    2     44      0
## 103     1     3  Tu1  Te5    Cd    3     11      0
## 104     1     3  Tu1  Te5    Cd    4     30      1
## 105     1     3  Tu1  Te5    Cd    5     34      0
## 106     1     3  Tu1  Te5    Cd    6      0      0
## 107     1     3  Tu1  Te5    Cd    7     29      1
## 108     1     3  Tu1  Te5    Cd    8     31      0
## 109     1     3  Tu1  Te5    Cd    9     35      0
## 110     1     3  Tu1  Te5    Cd   10      0      0
## 111     1     3  Tu1  Te5 water    1      0      0
## 112     1     3  Tu1  Te5 water    2      0      0
## 113     1     3  Tu1  Te5 water    3      0      0
## 114     1     3  Tu1  Te5 water    4      0      0
## 115     1     3  Tu1  Te5 water    5      0      0
## 116     1     3  Tu1  Te5 water    6     29      8
## 117     1     3  Tu1  Te5 water    7     36      9
## 118     1     3  Tu1  Te5 water    8     25     28
## 119     1     3  Tu1  Te5 water    9     16     46
## 120     1     3  Tu1  Te5 water   10      3      0
## 121     1     3  Tu2  Te4    Cd    1      1      0
## 122     1     3  Tu2  Te4    Cd    2      0      0
## 123     1     3  Tu2  Te4    Cd    3     17      2
## 124     1     3  Tu2  Te4    Cd    4      9      2
## 125     1     3  Tu2  Te4    Cd    5      0      0
## 126     1     3  Tu2  Te4    Cd    6      8      0
## 127     1     3  Tu2  Te4    Cd    7      0      0
## 128     1     3  Tu2  Te4    Cd    8      0      0
## 129     1     3  Tu2  Te4    Cd    9      0      0
## 130     1     3  Tu2  Te4    Cd   10      1      0
## 131     1     3  Tu2  Te4 water    1      0      0
## 132     1     3  Tu2  Te4 water    2      0      0
## 133     1     3  Tu2  Te4 water    3      0      0
## 134     1     3  Tu2  Te4 water    4      3      2
## 135     1     3  Tu2  Te4 water    5      0      0
## 136     1     3  Tu2  Te4 water    6     21     19
## 137     1     3  Tu2  Te4 water    7     53     23
## 138     1     3  Tu2  Te4 water    8     28     31
## 139     1     3  Tu2  Te4 water    9     30      1
## 140     1     3  Tu2  Te4 water   10     16      4
## 141     1     3  Tu2  Te5    Cd    1     48     10
## 142     1     3  Tu2  Te5    Cd    2     10      0
## 143     1     3  Tu2  Te5    Cd    3     14      1
## 144     1     3  Tu2  Te5    Cd    4     33      6
## 145     1     3  Tu2  Te5    Cd    5     19      2
## 146     1     3  Tu2  Te5    Cd    6     13      0
## 147     1     3  Tu2  Te5    Cd    7      8      0
## 148     1     3  Tu2  Te5    Cd    8      8      1
## 149     1     3  Tu2  Te5    Cd    9      4      0
## 150     1     3  Tu2  Te5    Cd   10     18      0
## 151     1     3  Tu2  Te5 water    1      0      0
## 152     1     3  Tu2  Te5 water    2      0      0
## 153     1     3  Tu2  Te5 water    3      0      0
## 154     1     3  Tu2  Te5 water    4      0      0
## 155     1     3  Tu2  Te5 water    5      0      0
## 156     1     3  Tu2  Te5 water    6      0      0
## 157     1     3  Tu2  Te5 water    7      1      2
## 158     1     3  Tu2  Te5 water    8      0      0
## 159     1     3  Tu2  Te5 water    9     18      4
## 160     1     3  Tu2  Te5 water   10      0      0
## 161     1     4  Tu1  Te4    Cd    1     18      0
## 162     1     4  Tu1  Te4    Cd    2      0      0
## 163     1     4  Tu1  Te4    Cd    3      0      0
## 164     1     4  Tu1  Te4    Cd    4      0      0
## 165     1     4  Tu1  Te4    Cd    5      0      2
## 166     1     4  Tu1  Te4    Cd    6      0      0
## 167     1     4  Tu1  Te4    Cd    7     91      2
## 168     1     4  Tu1  Te4    Cd    8     14      0
## 169     1     4  Tu1  Te4    Cd    9     22      0
## 170     1     4  Tu1  Te4    Cd   10     45      0
## 171     1     4  Tu1  Te4 water    1      6      7
## 172     1     4  Tu1  Te4 water    2      1      2
## 173     1     4  Tu1  Te4 water    3    174     45
## 174     1     4  Tu1  Te4 water    4      4      0
## 175     1     4  Tu1  Te4 water    5      2      1
## 176     1     4  Tu1  Te4 water    6      5      5
## 177     1     4  Tu1  Te4 water    7     32     58
## 178     1     4  Tu1  Te4 water    8     31     42
## 179     1     4  Tu1  Te4 water    9     18     70
## 180     1     4  Tu1  Te4 water   10     24     71
## 181     1     4  Tu1  Te5    Cd    1     22      0
## 182     1     4  Tu1  Te5    Cd    2      0      0
## 183     1     4  Tu1  Te5    Cd    3     17      1
## 184     1     4  Tu1  Te5    Cd    4      0      0
## 185     1     4  Tu1  Te5    Cd    5      3      0
## 186     1     4  Tu1  Te5    Cd    6      1      0
## 187     1     4  Tu1  Te5    Cd    7     55      0
## 188     1     4  Tu1  Te5    Cd    8     20      0
## 189     1     4  Tu1  Te5    Cd    9      0      0
## 190     1     4  Tu1  Te5    Cd   10     34      0
## 191     1     4  Tu1  Te5 water    1      0      0
## 192     1     4  Tu1  Te5 water    2      0      0
## 193     1     4  Tu1  Te5 water    3      1      0
## 194     1     4  Tu1  Te5 water    4      0      0
## 195     1     4  Tu1  Te5 water    5      0      0
## 196     1     4  Tu1  Te5 water    6     81     19
## 197     1     4  Tu1  Te5 water    7     52     11
## 198     1     4  Tu1  Te5 water    8     46     26
## 199     1     4  Tu1  Te5 water    9     22      3
## 200     1     4  Tu1  Te5 water   10     10      1
## 201     1     4  Tu2  Te4    Cd    1     39      6
## 202     1     4  Tu2  Te4    Cd    2      0      0
## 203     1     4  Tu2  Te4    Cd    3      7      5
## 204     1     4  Tu2  Te4    Cd    4     10      3
## 205     1     4  Tu2  Te4    Cd    5      0      0
## 206     1     4  Tu2  Te4    Cd    6     35      0
## 207     1     4  Tu2  Te4    Cd    7      0      0
## 208     1     4  Tu2  Te4    Cd    8     10      0
## 209     1     4  Tu2  Te4    Cd    9     32      0
## 210     1     4  Tu2  Te4    Cd   10     10      0
## 211     1     4  Tu2  Te4 water    1      0      0
## 212     1     4  Tu2  Te4 water    2      0      0
## 213     1     4  Tu2  Te4 water    3      0      0
## 214     1     4  Tu2  Te4 water    4      9     26
## 215     1     4  Tu2  Te4 water    5      0      0
## 216     1     4  Tu2  Te4 water    6      1      1
## 217     1     4  Tu2  Te4 water    7      0      0
## 218     1     4  Tu2  Te4 water    8    119     24
## 219     1     4  Tu2  Te4 water    9    137      0
## 220     1     4  Tu2  Te4 water   10      0      0
## 221     1     4  Tu2  Te5    Cd    1      0      0
## 222     1     4  Tu2  Te5    Cd    2      0      0
## 223     1     4  Tu2  Te5    Cd    3      9      0
## 224     1     4  Tu2  Te5    Cd    4      0      0
## 225     1     4  Tu2  Te5    Cd    5      0      0
## 226     1     4  Tu2  Te5    Cd    6      0      0
## 227     1     4  Tu2  Te5    Cd    7      0      0
## 228     1     4  Tu2  Te5    Cd    8     16      2
## 229     1     4  Tu2  Te5    Cd    9      1      0
## 230     1     4  Tu2  Te5    Cd   10     50     11
## 231     1     4  Tu2  Te5 water    1      0      0
## 232     1     4  Tu2  Te5 water    2      0      0
## 233     1     4  Tu2  Te5 water    3      0      0
## 234     1     4  Tu2  Te5 water    4      0      0
## 235     1     4  Tu2  Te5 water    5      0      0
## 236     1     4  Tu2  Te5 water    6      0      0
## 237     1     4  Tu2  Te5 water    7     63      9
## 238     1     4  Tu2  Te5 water    8      2      0
## 239     1     4  Tu2  Te5 water    9      2      0
## 240     1     4  Tu2  Te5 water   10      5      0
## 241     1     5  Tu1  Te4    Cd    1    206     22
## 242     1     5  Tu1  Te4    Cd    2      0      0
## 243     1     5  Tu1  Te4    Cd    3     61      7
## 244     1     5  Tu1  Te4    Cd    4     30      0
## 245     1     5  Tu1  Te4    Cd    5     21      0
## 246     1     5  Tu1  Te4    Cd    6     48      2
## 247     1     5  Tu1  Te4    Cd    7      8      1
## 248     1     5  Tu1  Te4    Cd    8     65      0
## 249     1     5  Tu1  Te4    Cd    9     17      0
## 250     1     5  Tu1  Te4    Cd   10    119      0
## 251     1     5  Tu1  Te4 water    1    116     33
## 252     1     5  Tu1  Te4 water    2     28      9
## 253     1     5  Tu1  Te4 water    3     24      6
## 254     1     5  Tu1  Te4 water    4    160     98
## 255     1     5  Tu1  Te4 water    5     17     25
## 256     1     5  Tu1  Te4 water    6     38     40
## 257     1     5  Tu1  Te4 water    7    103     37
## 258     1     5  Tu1  Te4 water    8    182     48
## 259     1     5  Tu1  Te4 water    9    278     58
## 260     1     5  Tu1  Te4 water   10    106     37
## 261     1     5  Tu1  Te5    Cd    1     42      2
## 262     1     5  Tu1  Te5    Cd    2     57      3
## 263     1     5  Tu1  Te5    Cd    3     57      7
## 264     1     5  Tu1  Te5    Cd    4    188     20
## 265     1     5  Tu1  Te5    Cd    5     61      2
## 266     1     5  Tu1  Te5    Cd    6    164      1
## 267     1     5  Tu1  Te5    Cd    7     30      0
## 268     1     5  Tu1  Te5    Cd    8     28      0
## 269     1     5  Tu1  Te5    Cd    9    101      0
## 270     1     5  Tu1  Te5    Cd   10    162      0
## 271     1     5  Tu1  Te5 water    1      0      0
## 272     1     5  Tu1  Te5 water    2      0      0
## 273     1     5  Tu1  Te5 water    3      0      0
## 274     1     5  Tu1  Te5 water    4      0      0
## 275     1     5  Tu1  Te5 water    5      0      0
## 276     1     5  Tu1  Te5 water    6     69     34
## 277     1     5  Tu1  Te5 water    7    160     76
## 278     1     5  Tu1  Te5 water    8     53     60
## 279     1     5  Tu1  Te5 water    9    137    102
## 280     1     5  Tu1  Te5 water   10    221    162
## 281     1     5  Tu2  Te4    Cd    1     96      6
## 282     1     5  Tu2  Te4    Cd    2      4      0
## 283     1     5  Tu2  Te4    Cd    3     35     35
## 284     1     5  Tu2  Te4    Cd    4     10      2
## 285     1     5  Tu2  Te4    Cd    5      0      0
## 286     1     5  Tu2  Te4    Cd    6     24      2
## 287     1     5  Tu2  Te4    Cd    7     24      0
## 288     1     5  Tu2  Te4    Cd    8     39      0
## 289     1     5  Tu2  Te4    Cd    9      7      0
## 290     1     5  Tu2  Te4    Cd   10      0      0
## 291     1     5  Tu2  Te4 water    1      0      0
## 292     1     5  Tu2  Te4 water    2      0      0
## 293     1     5  Tu2  Te4 water    3      0      0
## 294     1     5  Tu2  Te4 water    4      2      1
## 295     1     5  Tu2  Te4 water    5      0      0
## 296     1     5  Tu2  Te4 water    6     67     49
## 297     1     5  Tu2  Te4 water    7     49     49
## 298     1     5  Tu2  Te4 water    8    105     53
## 299     1     5  Tu2  Te4 water    9    125     25
## 300     1     5  Tu2  Te4 water   10    158     86
## 301     1     5  Tu2  Te5    Cd    1    104     53
## 302     1     5  Tu2  Te5    Cd    2    122      9
## 303     1     5  Tu2  Te5    Cd    3     11      5
## 304     1     5  Tu2  Te5    Cd    4     42     13
## 305     1     5  Tu2  Te5    Cd    5     46     86
## 306     1     5  Tu2  Te5    Cd    6     26      2
## 307     1     5  Tu2  Te5    Cd    7     18      1
## 308     1     5  Tu2  Te5    Cd    8     92      7
## 309     1     5  Tu2  Te5    Cd    9     45     12
## 310     1     5  Tu2  Te5    Cd   10     58      4
## 311     1     5  Tu2  Te5 water    1      0      0
## 312     1     5  Tu2  Te5 water    2      0      0
## 313     1     5  Tu2  Te5 water    3      0      0
## 314     1     5  Tu2  Te5 water    4      0      0
## 315     1     5  Tu2  Te5 water    5      0      0
## 316     1     5  Tu2  Te5 water    6     18      2
## 317     1     5  Tu2  Te5 water    7     74      4
## 318     1     5  Tu2  Te5 water    8      1      2
## 319     1     5  Tu2  Te5 water    9    327     11
## 320     1     5  Tu2  Te5 water   10     13      1
## 321     2     2  Tu1  Te4    Cd    1     23      0
## 322     2     2  Tu1  Te4    Cd    2     16      0
## 323     2     2  Tu1  Te4    Cd    3     18      0
## 324     2     2  Tu1  Te4    Cd    4      0      0
## 325     2     2  Tu1  Te4    Cd    5      1      0
## 326     2     2  Tu1  Te4    Cd    6     33      0
## 327     2     2  Tu1  Te4    Cd    7     80      0
## 328     2     2  Tu1  Te4    Cd    8     20      0
## 329     2     2  Tu1  Te4    Cd    9      0      0
## 330     2     2  Tu1  Te4    Cd   10      0      0
## 331     2     2  Tu1  Te4 water    1      0      0
## 332     2     2  Tu1  Te4 water    2      0      0
## 333     2     2  Tu1  Te4 water    3     89     90
## 334     2     2  Tu1  Te4 water    4     78     58
## 335     2     2  Tu1  Te4 water    5      0      0
## 336     2     2  Tu1  Te4 water    6      0      0
## 337     2     2  Tu1  Te4 water    7      1      1
## 338     2     2  Tu1  Te4 water    8     28     23
## 339     2     2  Tu1  Te4 water    9     15     21
## 340     2     2  Tu1  Te4 water   10     26      7
## 341     2     2  Tu1  Te5    Cd    1     56      7
## 342     2     2  Tu1  Te5    Cd    2     29      0
## 343     2     2  Tu1  Te5    Cd    3    146      7
## 344     2     2  Tu1  Te5    Cd    4      2      0
## 345     2     2  Tu1  Te5    Cd    5      4     13
## 346     2     2  Tu1  Te5    Cd    6      3      0
## 347     2     2  Tu1  Te5    Cd    7     19      0
## 348     2     2  Tu1  Te5    Cd    8     31      1
## 349     2     2  Tu1  Te5    Cd    9      8      0
## 350     2     2  Tu1  Te5    Cd   10      1      0
## 351     2     2  Tu1  Te5 water    1     47     10
## 352     2     2  Tu1  Te5 water    2     51     91
## 353     2     2  Tu1  Te5 water    3      0      0
## 354     2     2  Tu1  Te5 water    4     18     15
## 355     2     2  Tu1  Te5 water    5      0      0
## 356     2     2  Tu1  Te5 water    6     10     12
## 357     2     2  Tu1  Te5 water    7      1     18
## 358     2     2  Tu1  Te5 water    8     10      7
## 359     2     2  Tu1  Te5 water    9     26     31
## 360     2     2  Tu1  Te5 water   10     17     99
## 361     2     3  Tu1  Te4    Cd    1      4      0
## 362     2     3  Tu1  Te4    Cd    2     24      0
## 363     2     3  Tu1  Te4    Cd    3     22      1
## 364     2     3  Tu1  Te4    Cd    4     14      0
## 365     2     3  Tu1  Te4    Cd    5      4      0
## 366     2     3  Tu1  Te4    Cd    6     34      0
## 367     2     3  Tu1  Te4    Cd    7      0      0
## 368     2     3  Tu1  Te4    Cd    8     15      0
## 369     2     3  Tu1  Te4    Cd    9      1      0
## 370     2     3  Tu1  Te4    Cd   10      0      0
## 371     2     3  Tu1  Te4 water    1      0      0
## 372     2     3  Tu1  Te4 water    2      0      0
## 373     2     3  Tu1  Te4 water    3      0     13
## 374     2     3  Tu1  Te4 water    4      1      3
## 375     2     3  Tu1  Te4 water    5      0      0
## 376     2     3  Tu1  Te4 water    6      0      0
## 377     2     3  Tu1  Te4 water    7      0      0
## 378     2     3  Tu1  Te4 water    8      0      0
## 379     2     3  Tu1  Te4 water    9      6      8
## 380     2     3  Tu1  Te4 water   10     16      2
## 381     2     3  Tu1  Te5    Cd    1     59      8
## 382     2     3  Tu1  Te5    Cd    2     67      0
## 383     2     3  Tu1  Te5    Cd    3      0      0
## 384     2     3  Tu1  Te5    Cd    4     38      0
## 385     2     3  Tu1  Te5    Cd    5     10     25
## 386     2     3  Tu1  Te5    Cd    6      0      0
## 387     2     3  Tu1  Te5    Cd    7      0      2
## 388     2     3  Tu1  Te5    Cd    8     65      4
## 389     2     3  Tu1  Te5    Cd    9      0      0
## 390     2     3  Tu1  Te5    Cd   10      3      0
## 391     2     3  Tu1  Te5 water    1      1      2
## 392     2     3  Tu1  Te5 water    2     21    125
## 393     2     3  Tu1  Te5 water    3      1      0
## 394     2     3  Tu1  Te5 water    4      2      3
## 395     2     3  Tu1  Te5 water    5      0      0
## 396     2     3  Tu1  Te5 water    6     54     11
## 397     2     3  Tu1  Te5 water    7      0      4
## 398     2     3  Tu1  Te5 water    8      1      0
## 399     2     3  Tu1  Te5 water    9     47     23
## 400     2     3  Tu1  Te5 water   10     16     25
## 401     2     4  Tu1  Te4    Cd    1     17      0
## 402     2     4  Tu1  Te4    Cd    2      6      0
## 403     2     4  Tu1  Te4    Cd    3      4      0
## 404     2     4  Tu1  Te4    Cd    4     76      0
## 405     2     4  Tu1  Te4    Cd    5     13      0
## 406     2     4  Tu1  Te4    Cd    6      4      0
## 407     2     4  Tu1  Te4    Cd    7     44      0
## 408     2     4  Tu1  Te4    Cd    8     40      0
## 409     2     4  Tu1  Te4    Cd    9      0      0
## 410     2     4  Tu1  Te4    Cd   10      6      0
## 411     2     4  Tu1  Te4 water    1      0      0
## 412     2     4  Tu1  Te4 water    2      0      0
## 413     2     4  Tu1  Te4 water    3      1     22
## 414     2     4  Tu1  Te4 water    4      0      1
## 415     2     4  Tu1  Te4 water    5      0      0
## 416     2     4  Tu1  Te4 water    6      3      0
## 417     2     4  Tu1  Te4 water    7      2      1
## 418     2     4  Tu1  Te4 water    8      2      0
## 419     2     4  Tu1  Te4 water    9     42     68
## 420     2     4  Tu1  Te4 water   10      3      2
## 421     2     4  Tu1  Te5    Cd    1     54     17
## 422     2     4  Tu1  Te5    Cd    2     38      0
## 423     2     4  Tu1  Te5    Cd    3     77      2
## 424     2     4  Tu1  Te5    Cd    4     38      0
## 425     2     4  Tu1  Te5    Cd    5      2      0
## 426     2     4  Tu1  Te5    Cd    6     21      5
## 427     2     4  Tu1  Te5    Cd    7     12      0
## 428     2     4  Tu1  Te5    Cd    8     36      0
## 429     2     4  Tu1  Te5    Cd    9      0      0
## 430     2     4  Tu1  Te5    Cd   10     21      0
## 431     2     4  Tu1  Te5 water    1      0      0
## 432     2     4  Tu1  Te5 water    2    122    188
## 433     2     4  Tu1  Te5 water    3      0      0
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## 435     2     4  Tu1  Te5 water    5      7      3
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## 437     2     4  Tu1  Te5 water    7      5     18
## 438     2     4  Tu1  Te5 water    8      0      7
## 439     2     4  Tu1  Te5 water    9     45     70
## 440     2     4  Tu1  Te5 water   10      4      3
## 441     2     5  Tu1  Te4    Cd    1     11      0
## 442     2     5  Tu1  Te4    Cd    2     88      0
## 443     2     5  Tu1  Te4    Cd    3     87      0
## 444     2     5  Tu1  Te4    Cd    4      9      0
## 445     2     5  Tu1  Te4    Cd    5     29      0
## 446     2     5  Tu1  Te4    Cd    6     57      0
## 447     2     5  Tu1  Te4    Cd    7    180      0
## 448     2     5  Tu1  Te4    Cd    8    117      0
## 449     2     5  Tu1  Te4    Cd    9      8      0
## 450     2     5  Tu1  Te4    Cd   10     30      0
## 451     2     5  Tu1  Te4 water    1      0      0
## 452     2     5  Tu1  Te4 water    2      0      0
## 453     2     5  Tu1  Te4 water    3     49     66
## 454     2     5  Tu1  Te4 water    4      2      0
## 455     2     5  Tu1  Te4 water    5      0      0
## 456     2     5  Tu1  Te4 water    6      0      0
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## 458     2     5  Tu1  Te4 water    8     43     13
## 459     2     5  Tu1  Te4 water    9     40     26
## 460     2     5  Tu1  Te4 water   10    170     58
## 461     2     5  Tu1  Te5    Cd    1     23      2
## 462     2     5  Tu1  Te5    Cd    2     85      0
## 463     2     5  Tu1  Te5    Cd    3     10      0
## 464     2     5  Tu1  Te5    Cd    4     31      1
## 465     2     5  Tu1  Te5    Cd    5     81     27
## 466     2     5  Tu1  Te5    Cd    6     11      1
## 467     2     5  Tu1  Te5    Cd    7     26      2
## 468     2     5  Tu1  Te5    Cd    8    139      7
## 469     2     5  Tu1  Te5    Cd    9     40      0
## 470     2     5  Tu1  Te5    Cd   10     10      0
## 471     2     5  Tu1  Te5 water    1     44      4
## 472     2     5  Tu1  Te5 water    2     68     74
## 473     2     5  Tu1  Te5 water    3      6      0
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## 475     2     5  Tu1  Te5 water    5      0      0
## 476     2     5  Tu1  Te5 water    6     42     45
## 477     2     5  Tu1  Te5 water    7     54    100
## 478     2     5  Tu1  Te5 water    8     24     38
## 479     2     5  Tu1  Te5 water    9     43     70
## 480     2     5  Tu1  Te5 water   10    191    108
## 481     3     2  Tu1  Te4    Cd    1     31      2
## 482     3     2  Tu1  Te4    Cd    2      9     12
## 483     3     2  Tu1  Te4    Cd    3     75      0
## 484     3     2  Tu1  Te4    Cd    4     21      5
## 485     3     2  Tu1  Te4    Cd    5     56      0
## 486     3     2  Tu1  Te4    Cd    6     11      0
## 487     3     2  Tu1  Te4    Cd    7      1      0
## 488     3     2  Tu1  Te4    Cd    8    287      2
## 489     3     2  Tu1  Te4    Cd    9     12      0
## 490     3     2  Tu1  Te4    Cd   10     14      0
## 491     3     2  Tu1  Te4 water    1      3      0
## 492     3     2  Tu1  Te4 water    2      6      0
## 493     3     2  Tu1  Te4 water    3      0      0
## 494     3     2  Tu1  Te4 water    4      0      0
## 495     3     2  Tu1  Te4 water    5    120     14
## 496     3     2  Tu1  Te4 water    6     17     42
## 497     3     2  Tu1  Te4 water    7    202     20
## 498     3     2  Tu1  Te4 water    8     74     11
## 499     3     2  Tu1  Te4 water    9     76     64
## 500     3     2  Tu1  Te4 water   10    159     21
## 501     3     2  Tu1  Te5    Cd    1     29      0
## 502     3     2  Tu1  Te5    Cd    2     28      0
## 503     3     2  Tu1  Te5    Cd    3     50      0
## 504     3     2  Tu1  Te5    Cd    4     87      0
## 505     3     2  Tu1  Te5    Cd    5     52      0
## 506     3     2  Tu1  Te5    Cd    6     45      6
## 507     3     2  Tu1  Te5    Cd    7    116      0
## 508     3     2  Tu1  Te5    Cd    8     60      0
## 509     3     2  Tu1  Te5    Cd    9     65      3
## 510     3     2  Tu1  Te5    Cd   10    106     22
## 511     3     2  Tu1  Te5 water    1      0      0
## 512     3     2  Tu1  Te5 water    2      0      0
## 513     3     2  Tu1  Te5 water    3      0      0
## 514     3     2  Tu1  Te5 water    4      0      0
## 515     3     2  Tu1  Te5 water    5      0      0
## 516     3     2  Tu1  Te5 water    6      0      0
## 517     3     2  Tu1  Te5 water    7      0      0
## 518     3     2  Tu1  Te5 water    8     46      0
## 519     3     2  Tu1  Te5 water    9      0      0
## 520     3     2  Tu1  Te5 water   10      0      0
## 521     3     2  Tu2  Te4    Cd    1    129     34
## 522     3     2  Tu2  Te4    Cd    2     46      5
## 523     3     2  Tu2  Te4    Cd    3     36      4
## 524     3     2  Tu2  Te4    Cd    4     87      4
## 525     3     2  Tu2  Te4    Cd    5      0      0
## 526     3     2  Tu2  Te4    Cd    6     13      8
## 527     3     2  Tu2  Te4    Cd    7     11      7
## 528     3     2  Tu2  Te4    Cd    8     32      1
## 529     3     2  Tu2  Te4    Cd    9      8      4
## 530     3     2  Tu2  Te4    Cd   10     60      9
## 531     3     2  Tu2  Te4 water    1     84     23
## 532     3     2  Tu2  Te4 water    2     51     11
## 533     3     2  Tu2  Te4 water    3      1      0
## 534     3     2  Tu2  Te4 water    4    107      2
## 535     3     2  Tu2  Te4 water    5    112      4
## 536     3     2  Tu2  Te4 water    6      0      0
## 537     3     2  Tu2  Te4 water    7     51     18
## 538     3     2  Tu2  Te4 water    8      0      0
## 539     3     2  Tu2  Te4 water    9      0      0
## 540     3     2  Tu2  Te4 water   10      0      3
## 541     3     2  Tu2  Te5    Cd    1     95      0
## 542     3     2  Tu2  Te5    Cd    2     96      1
## 543     3     2  Tu2  Te5    Cd    3    113     17
## 544     3     2  Tu2  Te5    Cd    4     20      0
## 545     3     2  Tu2  Te5    Cd    5     69     19
## 546     3     2  Tu2  Te5    Cd    6     61      0
## 547     3     2  Tu2  Te5    Cd    7    202     15
## 548     3     2  Tu2  Te5    Cd    8     17      0
## 549     3     2  Tu2  Te5    Cd    9     24      0
## 550     3     2  Tu2  Te5    Cd   10      3      0
## 551     3     2  Tu2  Te5 water    1      1      0
## 552     3     2  Tu2  Te5 water    2      1      0
## 553     3     2  Tu2  Te5 water    3      0      0
## 554     3     2  Tu2  Te5 water    4      6     17
## 555     3     2  Tu2  Te5 water    5      0      0
## 556     3     2  Tu2  Te5 water    6     59     17
## 557     3     2  Tu2  Te5 water    7    210     14
## 558     3     2  Tu2  Te5 water    8     78     21
## 559     3     2  Tu2  Te5 water    9     48      2
## 560     3     2  Tu2  Te5 water   10      4      1
## 561     3     3  Tu1  Te4    Cd    1    100      1
## 562     3     3  Tu1  Te4    Cd    2     32      7
## 563     3     3  Tu1  Te4    Cd    3     47      4
## 564     3     3  Tu1  Te4    Cd    4     31      2
## 565     3     3  Tu1  Te4    Cd    5     31      0
## 566     3     3  Tu1  Te4    Cd    6     80      0
## 567     3     3  Tu1  Te4    Cd    7      0      0
## 568     3     3  Tu1  Te4    Cd    8     20      0
## 569     3     3  Tu1  Te4    Cd    9      4      0
## 570     3     3  Tu1  Te4    Cd   10     16      0
## 571     3     3  Tu1  Te4 water    1      3      0
## 572     3     3  Tu1  Te4 water    2      5      0
## 573     3     3  Tu1  Te4 water    3      0      0
## 574     3     3  Tu1  Te4 water    4      0      0
## 575     3     3  Tu1  Te4 water    5      5      0
## 576     3     3  Tu1  Te4 water    6     75     61
## 577     3     3  Tu1  Te4 water    7     84     41
## 578     3     3  Tu1  Te4 water    8     26     39
## 579     3     3  Tu1  Te4 water    9     88     52
## 580     3     3  Tu1  Te4 water   10     90     15
## 581     3     3  Tu1  Te5    Cd    1     10      0
## 582     3     3  Tu1  Te5    Cd    2     15      0
## 583     3     3  Tu1  Te5    Cd    3     34      0
## 584     3     3  Tu1  Te5    Cd    4     31      1
## 585     3     3  Tu1  Te5    Cd    5     57      0
## 586     3     3  Tu1  Te5    Cd    6      0      0
## 587     3     3  Tu1  Te5    Cd    7      0      0
## 588     3     3  Tu1  Te5    Cd    8      0      0
## 589     3     3  Tu1  Te5    Cd    9     37      2
## 590     3     3  Tu1  Te5    Cd   10      0      0
## 591     3     3  Tu1  Te5 water    1      0      0
## 592     3     3  Tu1  Te5 water    2      0      0
## 593     3     3  Tu1  Te5 water    3      0      0
## 594     3     3  Tu1  Te5 water    4      0      0
## 595     3     3  Tu1  Te5 water    5      0      0
## 596     3     3  Tu1  Te5 water    6      0      0
## 597     3     3  Tu1  Te5 water    7      0      0
## 598     3     3  Tu1  Te5 water    8      0      0
## 599     3     3  Tu1  Te5 water    9      0      0
## 600     3     3  Tu1  Te5 water   10      0      0
## 601     3     3  Tu2  Te4    Cd    1      2      0
## 602     3     3  Tu2  Te4    Cd    2      0      0
## 603     3     3  Tu2  Te4    Cd    3     19      6
## 604     3     3  Tu2  Te4    Cd    4     21      1
## 605     3     3  Tu2  Te4    Cd    5      0      0
## 606     3     3  Tu2  Te4    Cd    6      1      1
## 607     3     3  Tu2  Te4    Cd    7     16      1
## 608     3     3  Tu2  Te4    Cd    8     31      0
## 609     3     3  Tu2  Te4    Cd    9      0      0
## 610     3     3  Tu2  Te4    Cd   10     61      1
## 611     3     3  Tu2  Te4 water    1      1      3
## 612     3     3  Tu2  Te4 water    2     62     13
## 613     3     3  Tu2  Te4 water    3     72     71
## 614     3     3  Tu2  Te4 water    4    211     12
## 615     3     3  Tu2  Te4 water    5     15     10
## 616     3     3  Tu2  Te4 water    6      0      0
## 617     3     3  Tu2  Te4 water    7      0      0
## 618     3     3  Tu2  Te4 water    8      0      0
## 619     3     3  Tu2  Te4 water    9      0      0
## 620     3     3  Tu2  Te4 water   10      0      0
## 621     3     3  Tu2  Te5    Cd    1     32      3
## 622     3     3  Tu2  Te5    Cd    2      0      0
## 623     3     3  Tu2  Te5    Cd    3    111      2
## 624     3     3  Tu2  Te5    Cd    4     12      0
## 625     3     3  Tu2  Te5    Cd    5      2      0
## 626     3     3  Tu2  Te5    Cd    6      1      0
## 627     3     3  Tu2  Te5    Cd    7      1      1
## 628     3     3  Tu2  Te5    Cd    8      0      0
## 629     3     3  Tu2  Te5    Cd    9      0      0
## 630     3     3  Tu2  Te5    Cd   10      3      0
## 631     3     3  Tu2  Te5 water    1      0      0
## 632     3     3  Tu2  Te5 water    2      0      0
## 633     3     3  Tu2  Te5 water    3      0      0
## 634     3     3  Tu2  Te5 water    4      2      0
## 635     3     3  Tu2  Te5 water    5      0      0
## 636     3     3  Tu2  Te5 water    6      0      0
## 637     3     3  Tu2  Te5 water    7      0      0
## 638     3     3  Tu2  Te5 water    8      0      0
## 639     3     3  Tu2  Te5 water    9     25     34
## 640     3     3  Tu2  Te5 water   10      8     38
## 641     3     4  Tu1  Te4    Cd    1      6      1
## 642     3     4  Tu1  Te4    Cd    2     22     20
## 643     3     4  Tu1  Te4    Cd    3    109      2
## 644     3     4  Tu1  Te4    Cd    4     86      4
## 645     3     4  Tu1  Te4    Cd    5     68      1
## 646     3     4  Tu1  Te4    Cd    6    229      0
## 647     3     4  Tu1  Te4    Cd    7      5      0
## 648     3     4  Tu1  Te4    Cd    8     89      0
## 649     3     4  Tu1  Te4    Cd    9      1      0
## 650     3     4  Tu1  Te4    Cd   10      0      0
## 651     3     4  Tu1  Te4 water    1      1      1
## 652     3     4  Tu1  Te4 water    2      0      0
## 653     3     4  Tu1  Te4 water    3      0      0
## 654     3     4  Tu1  Te4 water    4      0      0
## 655     3     4  Tu1  Te4 water    5     39     11
## 656     3     4  Tu1  Te4 water    6    112     37
## 657     3     4  Tu1  Te4 water    7      0      0
## 658     3     4  Tu1  Te4 water    8     58     12
## 659     3     4  Tu1  Te4 water    9      0      0
## 660     3     4  Tu1  Te4 water   10      0      0
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## 663     3     4  Tu1  Te5    Cd    3     39      0
## 664     3     4  Tu1  Te5    Cd    4     81      0
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## 666     3     4  Tu1  Te5    Cd    6      3      0
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## 679     3     4  Tu1  Te5 water    9      0      0
## 680     3     4  Tu1  Te5 water   10      0      0
## 681     3     4  Tu2  Te4    Cd    1      0      0
## 682     3     4  Tu2  Te4    Cd    2      1      0
## 683     3     4  Tu2  Te4    Cd    3     22      6
## 684     3     4  Tu2  Te4    Cd    4      0      0
## 685     3     4  Tu2  Te4    Cd    5      0      0
## 686     3     4  Tu2  Te4    Cd    6      0      0
## 687     3     4  Tu2  Te4    Cd    7     31     29
## 688     3     4  Tu2  Te4    Cd    8     42      4
## 689     3     4  Tu2  Te4    Cd    9      9      3
## 690     3     4  Tu2  Te4    Cd   10      0      0
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## 699     3     4  Tu2  Te4 water    9      0      0
## 700     3     4  Tu2  Te4 water   10      2     10
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## 702     3     4  Tu2  Te5    Cd    2    226      2
## 703     3     4  Tu2  Te5    Cd    3      0      0
## 704     3     4  Tu2  Te5    Cd    4    121      7
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## 706     3     4  Tu2  Te5    Cd    6    223      3
## 707     3     4  Tu2  Te5    Cd    7      2      1
## 708     3     4  Tu2  Te5    Cd    8     60      1
## 709     3     4  Tu2  Te5    Cd    9     31      0
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## 719     3     4  Tu2  Te5 water    9      0      0
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## 723     3     5  Tu1  Te4    Cd    3    210      4
## 724     3     5  Tu1  Te4    Cd    4    115      6
## 725     3     5  Tu1  Te4    Cd    5    308      0
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## 728     3     5  Tu1  Te4    Cd    8      2      0
## 729     3     5  Tu1  Te4    Cd    9     12      0
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## 733     3     5  Tu1  Te4 water    3      0      0
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## 735     3     5  Tu1  Te4 water    5    266     38
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## 739     3     5  Tu1  Te4 water    9    251    214
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## 741     3     5  Tu1  Te5    Cd    1     26      0
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## 744     3     5  Tu1  Te5    Cd    4     98      1
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## 746     3     5  Tu1  Te5    Cd    6     21      1
## 747     3     5  Tu1  Te5    Cd    7    301      3
## 748     3     5  Tu1  Te5    Cd    8    207      0
## 749     3     5  Tu1  Te5    Cd    9    210      9
## 750     3     5  Tu1  Te5    Cd   10    312      7
## 751     3     5  Tu1  Te5 water    1      1      0
## 752     3     5  Tu1  Te5 water    2      0      0
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## 754     3     5  Tu1  Te5 water    4      0      0
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## 759     3     5  Tu1  Te5 water    9      0      0
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## 763     3     5  Tu2  Te4    Cd    3    181     10
## 764     3     5  Tu2  Te4    Cd    4    296     21
## 765     3     5  Tu2  Te4    Cd    5      2      0
## 766     3     5  Tu2  Te4    Cd    6     26     56
## 767     3     5  Tu2  Te4    Cd    7    134     40
## 768     3     5  Tu2  Te4    Cd    8    231     10
## 769     3     5  Tu2  Te4    Cd    9    168     11
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## 779     3     5  Tu2  Te4 water    9      0      0
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## 783     3     5  Tu2  Te5    Cd    3    204     10
## 784     3     5  Tu2  Te5    Cd    4      6      2
## 785     3     5  Tu2  Te5    Cd    5    161     35
## 786     3     5  Tu2  Te5    Cd    6    564     17
## 787     3     5  Tu2  Te5    Cd    7    287     17
## 788     3     5  Tu2  Te5    Cd    8    349      3
## 789     3     5  Tu2  Te5    Cd    9    210      1
## 790     3     5  Tu2  Te5    Cd   10      6      0
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## 799     3     5  Tu2  Te5 water    9    121     59
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## 804     4     2  Tu1  Te4    Cd    4      8      2
## 805     4     2  Tu1  Te4    Cd    5     19      0
## 806     4     2  Tu1  Te4    Cd    6      0      0
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## 808     4     2  Tu1  Te4    Cd    8     62      1
## 809     4     2  Tu1  Te4    Cd    9     23      2
## 810     4     2  Tu1  Te4    Cd   10      5      0
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## 823     4     2  Tu1  Te5    Cd    3      1      0
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## 829     4     2  Tu1  Te5    Cd    9     78      4
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## 839     4     2  Tu1  Te5 water    9      0      0
## 840     4     2  Tu1  Te5 water   10      0      0
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## 844     4     2  Tu2  Te4    Cd    4     54      3
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## 849     4     2  Tu2  Te4    Cd    9     87      9
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## 899     4     3  Tu1  Te4 water    9      3      1
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## 919     4     3  Tu1  Te5 water    9      0      0
## 920     4     3  Tu1  Te5 water   10      0      0
## 921     4     3  Tu2  Te4    Cd    1      4      0
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## 926     4     3  Tu2  Te4    Cd    6      0      0
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## 929     4     3  Tu2  Te4    Cd    9     20      6
## 930     4     3  Tu2  Te4    Cd   10      8      2
## 931     4     3  Tu2  Te4 water    1      0      0
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## 936     4     3  Tu2  Te4 water    6     89     13
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## 941     4     3  Tu2  Te5    Cd    1     16      0
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## 943     4     3  Tu2  Te5    Cd    3     62      6
## 944     4     3  Tu2  Te5    Cd    4     48      3
## 945     4     3  Tu2  Te5    Cd    5     99     15
## 946     4     3  Tu2  Te5    Cd    6     37      2
## 947     4     3  Tu2  Te5    Cd    7      5      0
## 948     4     3  Tu2  Te5    Cd    8      8      0
## 949     4     3  Tu2  Te5    Cd    9    128      3
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## 951     4     3  Tu2  Te5 water    1      0      0
## 952     4     3  Tu2  Te5 water    2      0      0
## 953     4     3  Tu2  Te5 water    3      0      0
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## 960     4     3  Tu2  Te5 water   10      1      0
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## 963     4     4  Tu1  Te4    Cd    3    272     24
## 964     4     4  Tu1  Te4    Cd    4     15      0
## 965     4     4  Tu1  Te4    Cd    5    165      0
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## 967     4     4  Tu1  Te4    Cd    7     98      0
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## 969     4     4  Tu1  Te4    Cd    9     55      0
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## 971     4     4  Tu1  Te4 water    1     10      1
## 972     4     4  Tu1  Te4 water    2    228    167
## 973     4     4  Tu1  Te4 water    3      0      0
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## 977     4     4  Tu1  Te4 water    7    102     19
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## 979     4     4  Tu1  Te4 water    9      0      0
## 980     4     4  Tu1  Te4 water   10     14      2
## 981     4     4  Tu1  Te5    Cd    1      0      0
## 982     4     4  Tu1  Te5    Cd    2     44      1
## 983     4     4  Tu1  Te5    Cd    3    198     10
## 984     4     4  Tu1  Te5    Cd    4     12      2
## 985     4     4  Tu1  Te5    Cd    5     24      0
## 986     4     4  Tu1  Te5    Cd    6     14      0
## 987     4     4  Tu1  Te5    Cd    7     50      1
## 988     4     4  Tu1  Te5    Cd    8      0      0
## 989     4     4  Tu1  Te5    Cd    9    123      7
## 990     4     4  Tu1  Te5    Cd   10     51      7
## 991     4     4  Tu1  Te5 water    1      0      0
## 992     4     4  Tu1  Te5 water    2      0      0
## 993     4     4  Tu1  Te5 water    3      1      2
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## 995     4     4  Tu1  Te5 water    5      2      6
## 996     4     4  Tu1  Te5 water    6      0      0
## 997     4     4  Tu1  Te5 water    7      0      0
## 998     4     4  Tu1  Te5 water    8      0      0
## 999     4     4  Tu1  Te5 water    9      0      0
## 1000    4     4  Tu1  Te5 water   10      0      0
## 1001    4     4  Tu2  Te4    Cd    1     33      1
## 1002    4     4  Tu2  Te4    Cd    2     28      4
## 1003    4     4  Tu2  Te4    Cd    3      0      0
## 1004    4     4  Tu2  Te4    Cd    4     75     15
## 1005    4     4  Tu2  Te4    Cd    5     20      1
## 1006    4     4  Tu2  Te4    Cd    6     97     26
## 1007    4     4  Tu2  Te4    Cd    7     23      8
## 1008    4     4  Tu2  Te4    Cd    8      6      6
## 1009    4     4  Tu2  Te4    Cd    9     75      1
## 1010    4     4  Tu2  Te4    Cd   10    129      9
## 1011    4     4  Tu2  Te4 water    1      0      0
## 1012    4     4  Tu2  Te4 water    2      0      0
## 1013    4     4  Tu2  Te4 water    3      0      0
## 1014    4     4  Tu2  Te4 water    4      0      0
## 1015    4     4  Tu2  Te4 water    5      0      0
## 1016    4     4  Tu2  Te4 water    6    284     48
## 1017    4     4  Tu2  Te4 water    7      6      1
## 1018    4     4  Tu2  Te4 water    8    235      9
## 1019    4     4  Tu2  Te4 water    9      8      2
## 1020    4     4  Tu2  Te4 water   10     73     12
## 1021    4     4  Tu2  Te5    Cd    1     19      0
## 1022    4     4  Tu2  Te5    Cd    2    124      3
## 1023    4     4  Tu2  Te5    Cd    3      9      0
## 1024    4     4  Tu2  Te5    Cd    4     55      1
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## 1029    4     4  Tu2  Te5    Cd    9     30      6
## 1030    4     4  Tu2  Te5    Cd   10    108      3
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## 1039    4     4  Tu2  Te5 water    9     14      1
## 1040    4     4  Tu2  Te5 water   10      0      0
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## 1042    4     5  Tu1  Te4    Cd    2     81     11
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## 1045    4     5  Tu1  Te4    Cd    5     84      0
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## 1047    4     5  Tu1  Te4    Cd    7    135      0
## 1048    4     5  Tu1  Te4    Cd    8    428      7
## 1049    4     5  Tu1  Te4    Cd    9    112      1
## 1050    4     5  Tu1  Te4    Cd   10     20      1
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## 1053    4     5  Tu1  Te4 water    3     17      1
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## 1059    4     5  Tu1  Te4 water    9      0      0
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## 1063    4     5  Tu1  Te5    Cd    3    331      6
## 1064    4     5  Tu1  Te5    Cd    4    259      1
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## 1079    4     5  Tu1  Te5 water    9      0      0
## 1080    4     5  Tu1  Te5 water   10    336      3
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## 1083    4     5  Tu2  Te4    Cd    3     22      1
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## 1085    4     5  Tu2  Te4    Cd    5    163      4
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## 1087    4     5  Tu2  Te4    Cd    7     78     12
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## 1099    4     5  Tu2  Te4 water    9    483     16
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## 1103    4     5  Tu2  Te5    Cd    3    123     19
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## 1107    4     5  Tu2  Te5    Cd    7     37      8
## 1108    4     5  Tu2  Te5    Cd    8     11      0
## 1109    4     5  Tu2  Te5    Cd    9     48     16
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## 1113    4     5  Tu2  Te5 water    3      0      0
## 1114    4     5  Tu2  Te5 water    4      0      0
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## 1116    4     5  Tu2  Te5 water    6     11      1
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## 1119    4     5  Tu2  Te5 water    9    383     12
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## 1129    5     2  Tu1  Te4    Cd    9     55      0
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## 1149    5     2  Tu1  Te5    Cd    9     20      0
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## 1161    5     2  Tu2  Te4    Cd    1      0      0
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## 1163    5     2  Tu2  Te4    Cd    3     12      0
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## 1169    5     2  Tu2  Te4    Cd    9     63      5
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## 1183    5     2  Tu2  Te5    Cd    3     34      0
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## 1189    5     2  Tu2  Te5    Cd    9    103      6
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## 1203    5     3  Tu1  Te4    Cd    3     23      0
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## 1363    5     5  Tu1  Te4    Cd    3     23      0
## 1364    5     5  Tu1  Te4    Cd    4     27      1
## 1365    5     5  Tu1  Te4    Cd    5      0      0
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## 1367    5     5  Tu1  Te4    Cd    7     49      1
## 1368    5     5  Tu1  Te4    Cd    8    299      8
## 1369    5     5  Tu1  Te4    Cd    9    136      7
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## 1381    5     5  Tu1  Te5    Cd    1    337      0
## 1382    5     5  Tu1  Te5    Cd    2    231      0
## 1383    5     5  Tu1  Te5    Cd    3     72     13
## 1384    5     5  Tu1  Te5    Cd    4    255      3
## 1385    5     5  Tu1  Te5    Cd    5    448      2
## 1386    5     5  Tu1  Te5    Cd    6    132      5
## 1387    5     5  Tu1  Te5    Cd    7    189     13
## 1388    5     5  Tu1  Te5    Cd    8    308      4
## 1389    5     5  Tu1  Te5    Cd    9    125      9
## 1390    5     5  Tu1  Te5    Cd   10    138     23
## 1391    5     5  Tu1  Te5 water    1    152     45
## 1392    5     5  Tu1  Te5 water    2    200    110
## 1393    5     5  Tu1  Te5 water    3    195    160
## 1394    5     5  Tu1  Te5 water    4    179     43
## 1395    5     5  Tu1  Te5 water    5    276     59
## 1396    5     5  Tu1  Te5 water    6    436    201
## 1397    5     5  Tu1  Te5 water    7    230     16
## 1398    5     5  Tu1  Te5 water    8    521     48
## 1399    5     5  Tu1  Te5 water    9     85     19
## 1400    5     5  Tu1  Te5 water   10    184     33
## 1401    5     5  Tu2  Te4    Cd    1     24      0
## 1402    5     5  Tu2  Te4    Cd    2     82      2
## 1403    5     5  Tu2  Te4    Cd    3     36      0
## 1404    5     5  Tu2  Te4    Cd    4     88      0
## 1405    5     5  Tu2  Te4    Cd    5     10      0
## 1406    5     5  Tu2  Te4    Cd    6      3      1
## 1407    5     5  Tu2  Te4    Cd    7      9     10
## 1408    5     5  Tu2  Te4    Cd    8     33      0
## 1409    5     5  Tu2  Te4    Cd    9     28      8
## 1410    5     5  Tu2  Te4    Cd   10     34      9
## 1411    5     5  Tu2  Te4 water    1    157     58
## 1412    5     5  Tu2  Te4 water    2    261     26
## 1413    5     5  Tu2  Te4 water    3    199     52
## 1414    5     5  Tu2  Te4 water    4     96     76
## 1415    5     5  Tu2  Te4 water    5    254     29
## 1416    5     5  Tu2  Te4 water    6    550     39
## 1417    5     5  Tu2  Te4 water    7    561     12
## 1418    5     5  Tu2  Te4 water    8    631      9
## 1419    5     5  Tu2  Te4 water    9    230     13
## 1420    5     5  Tu2  Te4 water   10    157      6
## 1421    5     5  Tu2  Te5    Cd    1     48      5
## 1422    5     5  Tu2  Te5    Cd    2     25      0
## 1423    5     5  Tu2  Te5    Cd    3      6      5
## 1424    5     5  Tu2  Te5    Cd    4     24      1
## 1425    5     5  Tu2  Te5    Cd    5     30      3
## 1426    5     5  Tu2  Te5    Cd    6    207     16
## 1427    5     5  Tu2  Te5    Cd    7    387     11
## 1428    5     5  Tu2  Te5    Cd    8    438      0
## 1429    5     5  Tu2  Te5    Cd    9    431      6
## 1430    5     5  Tu2  Te5    Cd   10    221      0
## 1431    5     5  Tu2  Te5 water    1    148     78
## 1432    5     5  Tu2  Te5 water    2    184     54
## 1433    5     5  Tu2  Te5 water    3    162     37
## 1434    5     5  Tu2  Te5 water    4    513     66
## 1435    5     5  Tu2  Te5 water    5    270     68
## 1436    5     5  Tu2  Te5 water    6    384     52
## 1437    5     5  Tu2  Te5 water    7    514      6
## 1438    5     5  Tu2  Te5 water    8    387     53
## 1439    5     5  Tu2  Te5 water    9    388     19
## 1440    5     5  Tu2  Te5 water   10    446    104
coex_g42_rep$Te_ratio<-sapply(c(1:dim(coex_g42_rep)[1]), function(x) coex_g42_rep$sum_Te[x]/sum(coex_g42_rep$sum_Tu[x],coex_g42_rep$sum_Te[x]))

#All the NAN were caused by division by 0, so we put it as 0
coex_g42_rep$Te_ratio[which(coex_g42_rep$Te_ratio=="NaN")]<-0

coex_g42_rep2<-coex_g42_rep %>%
  group_by(SRTu, SRTe, Rep2, Box2, Env) %>%
  summarize(sumTe=sum(sum_Te, na.rm=TRUE), sumTu=sum(sum_Tu, na.rm=TRUE))
## `summarise()` has grouped output by 'SRTu', 'SRTe', 'Rep2', 'Box2'. You can
## override using the `.groups` argument.
coex_g42_rep2$Te_ratio<-sapply(c(1:dim(coex_g42_rep2)[1]), function(x) coex_g42_rep2$sumTe[x]/sum(coex_g42_rep2$sumTu[x],coex_g42_rep2$sumTe[x]))

coex_g42_rep3<-coex_g42_rep2 %>%
  group_by(SRTu, SRTe, Rep2, Env) %>%
  summarize(sum_Te=sum(sumTe, na.rm=TRUE), sum_Tu=sum(sumTu, na.rm=TRUE), sdTe=sd(sumTe, na.rm=TRUE), sdTu=sd(sumTu, na.rm=TRUE), meanTeRatio=mean(Te_ratio, na.rm=TRUE))
## `summarise()` has grouped output by 'SRTu', 'SRTe', 'Rep2'. You can override
## using the `.groups` argument.
coex_g42_rep3$Te_ratio<-sapply(c(1:dim(coex_g42_rep3)[1]), function(x) coex_g42_rep3$sum_Te[x]/sum(coex_g42_rep3$sum_Tu[x],coex_g42_rep3$sum_Te[x]))

summarizing data

str(coex_g42_rep3)
## gropd_df [36 × 10] (S3: grouped_df/tbl_df/tbl/data.frame)
##  $ SRTu       : Factor w/ 2 levels "Tu1","Tu2": 1 1 1 1 1 1 1 1 1 1 ...
##  $ SRTe       : Factor w/ 2 levels "Te4","Te5": 1 1 1 1 1 1 1 1 1 1 ...
##  $ Rep2       : Factor w/ 5 levels "1","2","3","4",..: 1 1 2 2 3 3 4 4 5 5 ...
##  $ Env        : chr [1:36] "Cd" "water" "Cd" "water" ...
##  $ sum_Te     : int [1:36] 1436 1574 1135 624 2862 2487 2745 4329 1806 3285 ...
##  $ sum_Tu     : num [1:36] 95 909 1 486 129 ...
##  $ sdTe       : num [1:36] 117 92.7 87.2 73.9 185.5 ...
##  $ sdTu       : num [1:36] 15.565 55.419 0.316 64.907 26.396 ...
##  $ meanTeRatio: num [1:36] 0.958 0.624 0.999 0.648 0.938 ...
##  $ Te_ratio   : num [1:36] 0.938 0.634 0.999 0.562 0.957 ...
##  - attr(*, "groups")= tibble [18 × 4] (S3: tbl_df/tbl/data.frame)
##   ..$ SRTu : Factor w/ 2 levels "Tu1","Tu2": 1 1 1 1 1 1 1 1 1 1 ...
##   ..$ SRTe : Factor w/ 2 levels "Te4","Te5": 1 1 1 1 1 2 2 2 2 2 ...
##   ..$ Rep2 : Factor w/ 5 levels "1","2","3","4",..: 1 2 3 4 5 1 2 3 4 5 ...
##   ..$ .rows: list<int> [1:18] 
##   .. ..$ : int [1:2] 1 2
##   .. ..$ : int [1:2] 3 4
##   .. ..$ : int [1:2] 5 6
##   .. ..$ : int [1:2] 7 8
##   .. ..$ : int [1:2] 9 10
##   .. ..$ : int [1:2] 11 12
##   .. ..$ : int [1:2] 13 14
##   .. ..$ : int [1:2] 15 16
##   .. ..$ : int [1:2] 17 18
##   .. ..$ : int [1:2] 19 20
##   .. ..$ : int [1:2] 21 22
##   .. ..$ : int [1:2] 23 24
##   .. ..$ : int [1:2] 25 26
##   .. ..$ : int [1:2] 27 28
##   .. ..$ : int [1:2] 29 30
##   .. ..$ : int [1:2] 31 32
##   .. ..$ : int [1:2] 33 34
##   .. ..$ : int [1:2] 35 36
##   .. ..@ ptype: int(0) 
##   ..- attr(*, ".drop")= logi TRUE
coex_g42_rep3$Env<-plyr::mapvalues(coex_g42_rep3$Env, c("Cd","water"), c("Cd", "N"))
coex_g42_rep3$SRTu2<-plyr::mapvalues(coex_g42_rep3$SRTu, c("Tu1","Tu2"), c("SR1", "SR2"))
coex_g42_rep3$SRTe2<-plyr::mapvalues(coex_g42_rep3$SRTe, c("Te4","Te5"), c("SR4", "SR5"))

sum_observed_coex<-coex_g42_rep3
str(sum_observed_coex)
## gropd_df [36 × 12] (S3: grouped_df/tbl_df/tbl/data.frame)
##  $ SRTu       : Factor w/ 2 levels "Tu1","Tu2": 1 1 1 1 1 1 1 1 1 1 ...
##  $ SRTe       : Factor w/ 2 levels "Te4","Te5": 1 1 1 1 1 1 1 1 1 1 ...
##  $ Rep2       : Factor w/ 5 levels "1","2","3","4",..: 1 1 2 2 3 3 4 4 5 5 ...
##  $ Env        : chr [1:36] "Cd" "N" "Cd" "N" ...
##  $ sum_Te     : int [1:36] 1436 1574 1135 624 2862 2487 2745 4329 1806 3285 ...
##  $ sum_Tu     : num [1:36] 95 909 1 486 129 ...
##  $ sdTe       : num [1:36] 117 92.7 87.2 73.9 185.5 ...
##  $ sdTu       : num [1:36] 15.565 55.419 0.316 64.907 26.396 ...
##  $ meanTeRatio: num [1:36] 0.958 0.624 0.999 0.648 0.938 ...
##  $ Te_ratio   : num [1:36] 0.938 0.634 0.999 0.562 0.957 ...
##  $ SRTu2      : Factor w/ 2 levels "SR1","SR2": 1 1 1 1 1 1 1 1 1 1 ...
##  $ SRTe2      : Factor w/ 2 levels "SR4","SR5": 1 1 1 1 1 1 1 1 1 1 ...
##  - attr(*, "groups")= tibble [18 × 4] (S3: tbl_df/tbl/data.frame)
##   ..$ SRTu : Factor w/ 2 levels "Tu1","Tu2": 1 1 1 1 1 1 1 1 1 1 ...
##   ..$ SRTe : Factor w/ 2 levels "Te4","Te5": 1 1 1 1 1 2 2 2 2 2 ...
##   ..$ Rep2 : Factor w/ 5 levels "1","2","3","4",..: 1 2 3 4 5 1 2 3 4 5 ...
##   ..$ .rows: list<int> [1:18] 
##   .. ..$ : int [1:2] 1 2
##   .. ..$ : int [1:2] 3 4
##   .. ..$ : int [1:2] 5 6
##   .. ..$ : int [1:2] 7 8
##   .. ..$ : int [1:2] 9 10
##   .. ..$ : int [1:2] 11 12
##   .. ..$ : int [1:2] 13 14
##   .. ..$ : int [1:2] 15 16
##   .. ..$ : int [1:2] 17 18
##   .. ..$ : int [1:2] 19 20
##   .. ..$ : int [1:2] 21 22
##   .. ..$ : int [1:2] 23 24
##   .. ..$ : int [1:2] 25 26
##   .. ..$ : int [1:2] 27 28
##   .. ..$ : int [1:2] 29 30
##   .. ..$ : int [1:2] 31 32
##   .. ..$ : int [1:2] 33 34
##   .. ..$ : int [1:2] 35 36
##   .. ..@ ptype: int(0) 
##   ..- attr(*, ".drop")= logi TRUE
write.csv(sum_observed_coex, "./TableS3.csv")

Comparing to data

sum_observed_coex2<-sum_observed_coex %>%
  group_by(SRTu2, SRTe2, Env)%>%
  summarise(sumTe=sum(sum_Te, na.rm=TRUE),sumTu=mean(sum_Tu, na.rm=TRUE), sdTe2=sd(sum_Te, na.rm=TRUE)/sqrt(5), sdTu2=sd(sum_Tu, na.rm=TRUE)/sqrt(5), TeRatio=mean(meanTeRatio, na.rm=TRUE), sdTeRatio2=sd(meanTeRatio, na.rm=TRUE)/sqrt(5)) %>% as.data.frame()
## `summarise()` has grouped output by 'SRTu2', 'SRTe2'. You can override using
## the `.groups` argument.
sum_observed_coex2$TeRatio_L<-sum_observed_coex2$TeRatio-sum_observed_coex2$sdTeRatio2
sum_observed_coex2$TeRatio_U<-sum_observed_coex2$TeRatio+sum_observed_coex2$sdTeRatio2

¢## Testing predictions proportions

str(pred_coex_RK_REP)
## 'data.frame':    8 obs. of  15 variables:
##  $ SRTe     : chr  "SR4" "SR4" "SR4" "SR4" ...
##  $ SRTu     : chr  "SR1" "SR1" "SR2" "SR2" ...
##  $ Env      : chr  "N" "Cd" "N" "Cd" ...
##  $ predTu1  : num  9.86 6.47 10.13 7.15 10.44 ...
##  $ predTe1  : num  17.8 10.6 21.8 10.4 16.5 ...
##  $ predTu2  : num  9.05 6.59 7.91 7.88 11.64 ...
##  $ predTe2  : num  30.3 18 47.1 17.2 30.5 ...
##  $ predTu1_L: num  10.69 6.7 11.15 7.53 11.28 ...
##  $ predTe1_L: num  20.6 11.6 25.8 11.3 19.1 ...
##  $ predTu2_L: num  11.9 7.25 11.38 9.1 15.41 ...
##  $ predTe2_L: num  57.1 22.6 107.6 22 56.8 ...
##  $ predTu1_U: num  9.05 6.24 9.15 6.77 9.62 ...
##  $ predTe1_U: num  15.13 9.73 18.13 9.45 14.09 ...
##  $ predTu2_U: num  7.42 6.06 6.16 6.95 9.42 ...
##  $ predTe2_U: num  18.5 14.6 25.2 13.8 18.5 ...
pred_coex_RK_REP$TeRatio<-sapply(c(1:dim(pred_coex_RK_REP)[1]), function(x){
  pred_coex_RK_REP$predTe2[x]/(pred_coex_RK_REP$predTe2[x]+pred_coex_RK_REP$predTu2[x])
})

pred_coex_RK_w0$TeRatio<-sapply(c(1:dim(pred_coex_RK_w0)[1]), function(x){
  pred_coex_RK_w0$predTe2[x]/(pred_coex_RK_w0$predTe2[x]+pred_coex_RK_w0$predTu2[x])
})

pred_coex_RK_REP$TeRatio_L<-sapply(c(1:dim(pred_coex_RK_REP)[1]), function(x){
  pred_coex_RK_REP$predTe2_L[x]/(pred_coex_RK_REP$predTe2_L[x]+pred_coex_RK_REP$predTu2_L[x])
})

pred_coex_RK_w0$TeRatio_L<-sapply(c(1:dim(pred_coex_RK_w0)[1]), function(x){
  pred_coex_RK_w0$predTe2_L[x]/(pred_coex_RK_w0$predTe2_L[x]+pred_coex_RK_w0$predTu2_L[x])
})

pred_coex_RK_REP$TeRatio_U<-sapply(c(1:dim(pred_coex_RK_REP)[1]), function(x){
  pred_coex_RK_REP$predTe2_U[x]/(pred_coex_RK_REP$predTe2_U[x]+pred_coex_RK_REP$predTu2_U[x])
})

pred_coex_RK_w0$TeRatio_U<-sapply(c(1:dim(pred_coex_RK_w0)[1]), function(x){
  pred_coex_RK_w0$predTe2_U[x]/(pred_coex_RK_w0$predTe2_U[x]+pred_coex_RK_w0$predTu2_U[x])
})


str(pred_coex_RK_REP)
## 'data.frame':    8 obs. of  18 variables:
##  $ SRTe     : chr  "SR4" "SR4" "SR4" "SR4" ...
##  $ SRTu     : chr  "SR1" "SR1" "SR2" "SR2" ...
##  $ Env      : chr  "N" "Cd" "N" "Cd" ...
##  $ predTu1  : num  9.86 6.47 10.13 7.15 10.44 ...
##  $ predTe1  : num  17.8 10.6 21.8 10.4 16.5 ...
##  $ predTu2  : num  9.05 6.59 7.91 7.88 11.64 ...
##  $ predTe2  : num  30.3 18 47.1 17.2 30.5 ...
##  $ predTu1_L: num  10.69 6.7 11.15 7.53 11.28 ...
##  $ predTe1_L: num  20.6 11.6 25.8 11.3 19.1 ...
##  $ predTu2_L: num  11.9 7.25 11.38 9.1 15.41 ...
##  $ predTe2_L: num  57.1 22.6 107.6 22 56.8 ...
##  $ predTu1_U: num  9.05 6.24 9.15 6.77 9.62 ...
##  $ predTe1_U: num  15.13 9.73 18.13 9.45 14.09 ...
##  $ predTu2_U: num  7.42 6.06 6.16 6.95 9.42 ...
##  $ predTe2_U: num  18.5 14.6 25.2 13.8 18.5 ...
##  $ TeRatio  : num  0.77 0.732 0.856 0.686 0.724 ...
##  $ TeRatio_L: num  0.828 0.757 0.904 0.707 0.786 ...
##  $ TeRatio_U: num  0.713 0.707 0.804 0.665 0.662 ...
sum_pred_coex_RK_REP<-pred_coex_RK_REP %>%
  group_by(SRTu, SRTe, Env)%>%
  summarise(predTe=mean(predTe2, na.rm=TRUE),predTu=mean(predTu2, na.rm=TRUE), sumTeRatio=(sum(predTe2, na.rm=TRUE)/(sum(predTe2, na.rm=TRUE)+sum(predTu2, na.rm=TRUE)))) %>% as.data.frame()
## `summarise()` has grouped output by 'SRTu', 'SRTe'. You can override using the
## `.groups` argument.

Comparing to proportions

str(sum_observed_coex)
## gropd_df [36 × 12] (S3: grouped_df/tbl_df/tbl/data.frame)
##  $ SRTu       : Factor w/ 2 levels "Tu1","Tu2": 1 1 1 1 1 1 1 1 1 1 ...
##  $ SRTe       : Factor w/ 2 levels "Te4","Te5": 1 1 1 1 1 1 1 1 1 1 ...
##  $ Rep2       : Factor w/ 5 levels "1","2","3","4",..: 1 1 2 2 3 3 4 4 5 5 ...
##  $ Env        : chr [1:36] "Cd" "N" "Cd" "N" ...
##  $ sum_Te     : int [1:36] 1436 1574 1135 624 2862 2487 2745 4329 1806 3285 ...
##  $ sum_Tu     : num [1:36] 95 909 1 486 129 ...
##  $ sdTe       : num [1:36] 117 92.7 87.2 73.9 185.5 ...
##  $ sdTu       : num [1:36] 15.565 55.419 0.316 64.907 26.396 ...
##  $ meanTeRatio: num [1:36] 0.958 0.624 0.999 0.648 0.938 ...
##  $ Te_ratio   : num [1:36] 0.938 0.634 0.999 0.562 0.957 ...
##  $ SRTu2      : Factor w/ 2 levels "SR1","SR2": 1 1 1 1 1 1 1 1 1 1 ...
##  $ SRTe2      : Factor w/ 2 levels "SR4","SR5": 1 1 1 1 1 1 1 1 1 1 ...
##  - attr(*, "groups")= tibble [18 × 4] (S3: tbl_df/tbl/data.frame)
##   ..$ SRTu : Factor w/ 2 levels "Tu1","Tu2": 1 1 1 1 1 1 1 1 1 1 ...
##   ..$ SRTe : Factor w/ 2 levels "Te4","Te5": 1 1 1 1 1 2 2 2 2 2 ...
##   ..$ Rep2 : Factor w/ 5 levels "1","2","3","4",..: 1 2 3 4 5 1 2 3 4 5 ...
##   ..$ .rows: list<int> [1:18] 
##   .. ..$ : int [1:2] 1 2
##   .. ..$ : int [1:2] 3 4
##   .. ..$ : int [1:2] 5 6
##   .. ..$ : int [1:2] 7 8
##   .. ..$ : int [1:2] 9 10
##   .. ..$ : int [1:2] 11 12
##   .. ..$ : int [1:2] 13 14
##   .. ..$ : int [1:2] 15 16
##   .. ..$ : int [1:2] 17 18
##   .. ..$ : int [1:2] 19 20
##   .. ..$ : int [1:2] 21 22
##   .. ..$ : int [1:2] 23 24
##   .. ..$ : int [1:2] 25 26
##   .. ..$ : int [1:2] 27 28
##   .. ..$ : int [1:2] 29 30
##   .. ..$ : int [1:2] 31 32
##   .. ..$ : int [1:2] 33 34
##   .. ..$ : int [1:2] 35 36
##   .. ..@ ptype: int(0) 
##   ..- attr(*, ".drop")= logi TRUE
sum_observed_coex_rep2<-sum_observed_coex %>%
  group_by(SRTe, SRTu, Env) %>%
  summarize(obs_TeRatio=mean(meanTeRatio), SE_obs=sd(meanTeRatio)/sqrt(5), meanTe=mean(sum_Te, na.rm=TRUE), meanTu=mean(sum_Tu, na.rm=TRUE)) %>% as.data.frame()
## `summarise()` has grouped output by 'SRTe', 'SRTu'. You can override using the
## `.groups` argument.
sum_observed_coex_rep2$SRTe2<-(plyr::mapvalues(as.character(sum_observed_coex_rep2$SRTe), c("Te4","Te5"), c("SR4", "SR5")))
sum_observed_coex_rep2$SRTu2<-(plyr::mapvalues(as.character(sum_observed_coex_rep2$SRTu), c("Tu1","Tu2"), c("SR1", "SR2")))
colnames(sum_observed_coex_rep2)[c(1:2, 8,9)]<-c("SRTe2", "SRTu2","SRTe", "SRTu" )

sum_observed_coex_rep2<-sum_observed_coex_rep2[,c(8,9,3:7)]
colnames(sum_observed_coex)[c(1,2,3,11:12)]<-c("SRTu2","SRTe2","Replicate","SRTu","SRTe")

sum_observed_coex_rep<-inner_join(sum_observed_coex_rep2, pred_coex_RK_REP, by=c("SRTe", "SRTu", "Env"))

sum_observed_coex_rep<-as.data.frame(sum_observed_coex_rep[,c("SRTe", "SRTu", "Env", "obs_TeRatio","SE_obs", "TeRatio", "TeRatio_L", "TeRatio_U", "meanTe","meanTu", "predTu2","predTe2")])

str(sum_observed_coex_rep)
## 'data.frame':    8 obs. of  12 variables:
##  $ SRTe       : chr  "SR4" "SR4" "SR4" "SR4" ...
##  $ SRTu       : chr  "SR1" "SR1" "SR2" "SR2" ...
##  $ Env        : chr  "Cd" "N" "Cd" "N" ...
##  $ obs_TeRatio: num  0.963 0.707 0.894 0.737 0.956 ...
##  $ SE_obs     : num  0.01 0.0308 0.0222 0.0378 0.0111 ...
##  $ TeRatio    : num  0.732 0.77 0.686 0.856 0.569 ...
##  $ TeRatio_L  : num  0.757 0.828 0.707 0.904 0.587 ...
##  $ TeRatio_U  : num  0.707 0.713 0.665 0.804 0.552 ...
##  $ meanTe     : num  1997 2460 1603 3022 2881 ...
##  $ meanTu     : num  88.6 1088.6 198 810.5 109.8 ...
##  $ predTu2    : num  6.59 9.05 7.88 7.91 7.99 ...
##  $ predTe2    : num  18 30.3 17.2 47.1 10.6 ...
colnames(sum_observed_coex_rep)[6:8]<-c("pred_T1", "T1_L","T1_U")

pred_coex_RK_w0$Replicate<-as.factor(pred_coex_RK_w0$Replicate)

sum_observed_coex_ALL<-inner_join(sum_observed_coex, pred_coex_RK_w0, by=c("SRTe", "SRTu", "Env", "Replicate"))

sum2_observed_coex_ALL<-as.data.frame(sum_observed_coex_ALL[,c(11,12,3,4,5,6,9,15,16)])

str(sum2_observed_coex_ALL)
## 'data.frame':    36 obs. of  9 variables:
##  $ SRTu       : chr  "SR1" "SR1" "SR1" "SR1" ...
##  $ SRTe       : chr  "SR4" "SR4" "SR4" "SR4" ...
##  $ Replicate  : Factor w/ 5 levels "1","2","3","4",..: 1 1 2 2 3 3 4 4 5 5 ...
##  $ Env        : chr  "Cd" "N" "Cd" "N" ...
##  $ sum_Te     : int  1436 1574 1135 624 2862 2487 2745 4329 1806 3285 ...
##  $ sum_Tu     : num  95 909 1 486 129 ...
##  $ meanTeRatio: num  0.958 0.624 0.999 0.648 0.938 ...
##  $ predTu2    : num  5.46 8.02 7.78 22.15 7.93 ...
##  $ predTe2    : num  20.19 21.84 22.13 4.57 10.88 ...
sum2_observed_coex_ALL$predTeRatio<-sapply(c(1:dim(sum2_observed_coex_ALL)[1]), function(x){sum2_observed_coex_ALL$predTe2[x]/sum(sum2_observed_coex_ALL$predTe2[x],sum2_observed_coex_ALL$predTu2[x])})

Testing pooled replicates

m3<- glm(cbind(meanTe, meanTu)~pred_T1, data=sum_observed_coex_rep, family="binomial")
## Warning in eval(family$initialize): non-integer counts in a binomial glm!
m4<- glm(obs_TeRatio~pred_T1, data=sum_observed_coex_rep, family="binomial")
## Warning in eval(family$initialize): non-integer #successes in a binomial glm!
summary(m4)
## 
## Call:
## glm(formula = obs_TeRatio ~ pred_T1, family = "binomial", data = sum_observed_coex_rep)
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)
## (Intercept)    5.702      8.805   0.648    0.517
## pred_T1       -5.727     11.988  -0.478    0.633
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 0.72177  on 7  degrees of freedom
## Residual deviance: 0.48675  on 6  degrees of freedom
## AIC: 7.034
## 
## Number of Fisher Scoring iterations: 5
summary(m3)
## 
## Call:
## glm(formula = cbind(meanTe, meanTu) ~ pred_T1, family = "binomial", 
##     data = sum_observed_coex_rep)
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)    5.405      0.159    34.0   <2e-16 ***
## pred_T1       -5.238      0.213   -24.6   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 1980.4  on 7  degrees of freedom
## Residual deviance: 1348.9  on 6  degrees of freedom
## AIC: 1415
## 
## Number of Fisher Scoring iterations: 5
summary(m4)
## 
## Call:
## glm(formula = obs_TeRatio ~ pred_T1, family = "binomial", data = sum_observed_coex_rep)
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)
## (Intercept)    5.702      8.805   0.648    0.517
## pred_T1       -5.727     11.988  -0.478    0.633
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 0.72177  on 7  degrees of freedom
## Residual deviance: 0.48675  on 6  degrees of freedom
## AIC: 7.034
## 
## Number of Fisher Scoring iterations: 5
emtrends(m3, var="pred_T1", type="response")
## 'emmGrid' object with variables:
##     pred_T1 = 0.70686
emtrends(m4, var="pred_T1", type="response")
## 'emmGrid' object with variables:
##     pred_T1 = 0.70686
m5<-glm(cbind(meanTe, meanTu)~0+pred_T1, data=sum_observed_coex_rep, family="binomial")
## Warning in eval(family$initialize): non-integer counts in a binomial glm!
summary(m5)
## 
## Call:
## glm(formula = cbind(meanTe, meanTu) ~ 0 + pred_T1, family = "binomial", 
##     data = sum_observed_coex_rep)
## 
## Coefficients:
##         Estimate Std. Error z value Pr(>|z|)    
## pred_T1  2.12736    0.02484   85.64   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 12352  on 8  degrees of freedom
## Residual deviance:  2627  on 7  degrees of freedom
## AIC: 2690
## 
## Number of Fisher Scoring iterations: 5
emtrends(m5, var="pred_T1", type="response")
## 'emmGrid' object with variables:
##     pred_T1 = 0.70686
sum_observed_coex_rep<-sum_observed_coex_rep %>% mutate(yhat=predict(m5))

Testing per replicate

sum_observed_coex_ALL2<-sum2_observed_coex_ALL %>%
  group_by(SRTe, SRTu, Env) %>%
  summarize(meanRatio=mean(meanTeRatio, na.rm=TRUE), mean_pred=mean(predTeRatio, na.rm=TRUE), sdRatio=sd(meanTeRatio, na.rm=TRUE)/sqrt(5), sdPred=sd(predTeRatio, na.rm=TRUE)/sqrt(5), meanTe=mean(sum_Te, na.rm=TRUE), meanTu=mean(sum_Tu, na.rm=TRUE))
## `summarise()` has grouped output by 'SRTe', 'SRTu'. You can override using the
## `.groups` argument.
m4<- glmmTMB(cbind(meanTe, meanTu)~mean_pred*Env, data=sum_observed_coex_ALL2, family=binomial(link="logit"))
## Warning in eval(family$initialize): non-integer counts in a binomial glm!
summary(m4)
##  Family: binomial  ( logit )
## Formula:          cbind(meanTe, meanTu) ~ mean_pred * Env
## Data: sum_observed_coex_ALL2
## 
##      AIC      BIC   logLik deviance df.resid 
##    407.8    408.1   -199.9    399.8        4 
## 
## 
## Conditional model:
##                Estimate Std. Error z value Pr(>|z|)    
## (Intercept)      4.0171     0.4143   9.695  < 2e-16 ***
## mean_pred       -1.9980     0.6353  -3.145  0.00166 ** 
## EnvN            -3.7002     0.4296  -8.613  < 2e-16 ***
## mean_pred:EnvN   3.1957     0.6599   4.843 1.28e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# This is from the summary of the model
 slope_all<-invlogit(1.4211)
 slope_ci_L<-invlogit(1.4211)-0.1861
 slope_ci_U<-invlogit(1.4211)+0.1861
 

ggplot(sum_observed_coex_ALL2, aes(x=meanRatio,y=mean_pred))+
  #geom_smooth(method="glm", colour="black", fullrange=TRUE, family="binomial")+
  geom_abline(intercept = 0, slope=slope_all)+
  geom_abline(intercept = 0, slope=slope_ci_L, linetype="dashed")+
  geom_abline(intercept = 0, slope=slope_ci_U, linetype="dashed")+
  #geom_abline(intercept = 0, slope=0.7)+
  geom_errorbar(aes(ymin=mean_pred-sdPred, ymax=mean_pred+sdPred), width=0.02, colour="black")+
  geom_errorbarh(aes(xmin=meanRatio-sdRatio, xmax=meanRatio+sdRatio), height=0.03, colour="black")+
  geom_point(size=3, aes(fill=interaction(SRTu, SRTe), shape=Env))+
   scale_fill_manual(values=c("#D7191C", "#FDAE61" ,"#ABDDA4", "#2B83BA"), labels=c("Te no cadmium:Tu no cadmium", "Te cadmium: Tu no cadmium", "Te no cadmium: Tu cadmium", "Te cadmium: Tu cadmium"))+
  scale_shape_manual(values=c(22,23))+
    theme_ines+
  xlab("Observed ratio")+
  ylab("Predicted ratio")+
  ylim(c(0.3,1))+
  xlim(c(0.55,1))+
  theme(legend.position = "none")

save_plot("./Analyses/cxr_normal_REP/Fig4.pdf", width=10, height=10)


write.csv(pred_coex_RK_w0, "./PredictedPerReplicate.csv")
write.csv(pred_coex_RK_REP, "./PredictedPooledReplicate.csv")

5 - Simulations for figure 1

pred_coex1Gen<-as.data.frame(expand_grid(Te=c("SR4","SR5"), Tu=c("SR1", "SR2"), Environment= c("N", "Cd")))


pred_coex1Gen$predTu_onlyLambda<-sapply(c(1:length(pred_coex1Gen$Tu)), function(x){
  aux_alphas<-subset(param_all_REP, Tu_Regime==as.character(pred_coex1Gen$Tu[x]) & Te_Regime==as.character(pred_coex1Gen$Te[x]) & Environment==as.character(pred_coex1Gen$Environment[x]))

  bl<-aux_alphas$Tu_lambda[1]*10
  
  bl
  })

pred_coex1Gen$predTu_Lambda_INTRA<-sapply(c(1:length(pred_coex1Gen$Tu)), function(x){
  aux_alphas<-subset(param_all_REP, Tu_Regime==as.character(pred_coex1Gen$Tu[x]) & Te_Regime==as.character(pred_coex1Gen$Te[x]) & Environment==as.character(pred_coex1Gen$Environment[x]))

  bl<-aux_alphas$Tu_lambda[1]*10*exp(-aux_alphas$Tu_intra[1]*10)
  
  bl
  })

pred_coex1Gen$predTu_ALL<-sapply(c(1:length(pred_coex1Gen$Tu)), function(x){
  aux_alphas<-subset(param_all_REP, Tu_Regime==as.character(pred_coex1Gen$Tu[x]) & Te_Regime==as.character(pred_coex1Gen$Te[x]) & Environment==as.character(pred_coex1Gen$Environment[x]))

  bl<-aux_alphas$Tu_lambda[1]*10*exp(-aux_alphas$Tu_intra[1]*10- aux_alphas$Tu_inter[1]*10)
  
  bl
  })


pred_coex1Gen$predTe_onlyLambda<-sapply(c(1:length(pred_coex1Gen$Tu)), function(x){
  aux_alphas<-subset(param_all_REP, Tu_Regime==as.character(pred_coex1Gen$Tu[x]) & Te_Regime==as.character(pred_coex1Gen$Te[x]) & Environment==as.character(pred_coex1Gen$Environment[x]))

  bl<-aux_alphas$Te_lambda[1]*10
  
  bl
  })

pred_coex1Gen$predTe_Lambda_INTRA<-sapply(c(1:length(pred_coex1Gen$Tu)), function(x){
  aux_alphas<-subset(param_all_REP, Tu_Regime==as.character(pred_coex1Gen$Tu[x]) & Te_Regime==as.character(pred_coex1Gen$Te[x]) & Environment==as.character(pred_coex1Gen$Environment[x]))

  bl<-aux_alphas$Te_lambda[1]*10*exp(-aux_alphas$Te_intra[1]*10)
  
  bl
  })

pred_coex1Gen$predTe_ALL<-sapply(c(1:length(pred_coex1Gen$Tu)), function(x){
  aux_alphas<-subset(param_all_REP, Tu_Regime==as.character(pred_coex1Gen$Tu[x]) & Te_Regime==as.character(pred_coex1Gen$Te[x]) & Environment==as.character(pred_coex1Gen$Environment[x]))

  bl<-aux_alphas$Te_lambda[1]*10*exp(-aux_alphas$Te_intra[1]*10- aux_alphas$Te_inter[1]*10)
  
  bl
  })

pred_coex1Gen$Control_lambdaTu<-sapply(c(1:dim(pred_coex1Gen)[1]), function(x){
  cont<-subset(pred_coex1Gen, Environment==pred_coex1Gen$Environment[x] & Tu=="SR1")
  
  pred_coex1Gen$predTu_onlyLambda[x]/cont$predTu_onlyLambda[1]
  
})

pred_coex1Gen$Control_lambdaTe<-sapply(c(1:dim(pred_coex1Gen)[1]), function(x){
  cont<-subset(pred_coex1Gen, Environment==pred_coex1Gen$Environment[x] & Te=="SR4")
  
  pred_coex1Gen$predTe_onlyLambda[x]/cont$predTe_onlyLambda[1]
  
})

pred_coex1Gen$Control_lambdaIntraTu<-sapply(c(1:dim(pred_coex1Gen)[1]), function(x){
  cont<-subset(pred_coex1Gen, Environment==pred_coex1Gen$Environment[x] & Te=="SR4" & Tu=="SR1")
  
  pred_coex1Gen$predTu_Lambda_INTRA[x]/cont$predTu_Lambda_INTRA[1]
  
})

pred_coex1Gen$Control_lambdaIntraTe<-sapply(c(1:dim(pred_coex1Gen)[1]), function(x){
  cont<-subset(pred_coex1Gen, Environment==pred_coex1Gen$Environment[x] & Te=="SR4" & Tu=="SR1")
  
  pred_coex1Gen$predTe_Lambda_INTRA[x]/cont$predTe_Lambda_INTRA[1]
  
})

pred_coex1Gen$Control_ALLTu<-sapply(c(1:dim(pred_coex1Gen)[1]), function(x){
  cont<-subset(pred_coex1Gen, Environment==pred_coex1Gen$Environment[x] & Te=="SR4" & Tu=="SR1")
  
  pred_coex1Gen$predTu_ALL[x]/cont$predTu_ALL[1]
  
})

pred_coex1Gen$Control_ALLTe<-sapply(c(1:dim(pred_coex1Gen)[1]), function(x){
  cont<-subset(pred_coex1Gen, Environment==pred_coex1Gen$Environment[x] & Te=="SR4" & Tu=="SR1")
  
  pred_coex1Gen$predTe_ALL[x]/cont$predTe_ALL[1]
  
})

Lower

pred_coex1Gen$predTu_onlyLambda_L<-sapply(c(1:length(pred_coex1Gen$Tu)), function(x){
  aux_alphas<-subset(param_all_REP_lower, Tu_Regime==as.character(pred_coex1Gen$Tu[x]) & Te_Regime==as.character(pred_coex1Gen$Te[x]) & Environment==as.character(pred_coex1Gen$Environment[x]))

  bl<-aux_alphas$Tu_lambda[1]*10
  
  bl
  })

pred_coex1Gen$predTu_Lambda_INTRA_L<-sapply(c(1:length(pred_coex1Gen$Tu)), function(x){
  aux_alphas<-subset(param_all_REP_upper, Tu_Regime==as.character(pred_coex1Gen$Tu[x]) & Te_Regime==as.character(pred_coex1Gen$Te[x]) & Environment==as.character(pred_coex1Gen$Environment[x]))
  aux_lambdas<-subset(param_all_REP_lower, Tu_Regime==as.character(pred_coex1Gen$Tu[x]) & Te_Regime==as.character(pred_coex1Gen$Te[x]) & Environment==as.character(pred_coex1Gen$Environment[x]))

  bl<-aux_lambdas$Tu_lambda[1]*10*exp(-aux_alphas$Tu_intra[1]*10)
  
  bl
  })

pred_coex1Gen$predTu_ALL_L<-sapply(c(1:length(pred_coex1Gen$Tu)), function(x){
  aux_alphas<-subset(param_all_REP_upper, Tu_Regime==as.character(pred_coex1Gen$Tu[x]) & Te_Regime==as.character(pred_coex1Gen$Te[x]) & Environment==as.character(pred_coex1Gen$Environment[x]))
  aux_lambdas<-subset(param_all_REP_lower, Tu_Regime==as.character(pred_coex1Gen$Tu[x]) & Te_Regime==as.character(pred_coex1Gen$Te[x]) & Environment==as.character(pred_coex1Gen$Environment[x]))

  bl<-aux_lambdas$Tu_lambda[1]*10*exp(-aux_alphas$Tu_intra[1]*10- aux_alphas$Tu_inter[1]*10)
  
  bl
  })


pred_coex1Gen$predTe_onlyLambda_L<-sapply(c(1:length(pred_coex1Gen$Tu)), function(x){
  aux_alphas<-subset(param_all_REP_lower, Tu_Regime==as.character(pred_coex1Gen$Tu[x]) & Te_Regime==as.character(pred_coex1Gen$Te[x]) & Environment==as.character(pred_coex1Gen$Environment[x]))

  bl<-aux_alphas$Te_lambda[1]*10
  
  bl
  })

pred_coex1Gen$predTe_Lambda_INTRA_L<-sapply(c(1:length(pred_coex1Gen$Tu)), function(x){
  aux_alphas<-subset(param_all_REP_upper, Tu_Regime==as.character(pred_coex1Gen$Tu[x]) & Te_Regime==as.character(pred_coex1Gen$Te[x]) & Environment==as.character(pred_coex1Gen$Environment[x]))
  aux_lambdas<-subset(param_all_REP_lower, Tu_Regime==as.character(pred_coex1Gen$Tu[x]) & Te_Regime==as.character(pred_coex1Gen$Te[x]) & Environment==as.character(pred_coex1Gen$Environment[x]))

  bl<-aux_lambdas$Te_lambda[1]*10*exp(-aux_alphas$Te_intra[1]*10)
  
  bl
  })

pred_coex1Gen$predTe_ALL_L<-sapply(c(1:length(pred_coex1Gen$Tu)), function(x){
  aux_alphas<-subset(param_all_REP_upper, Tu_Regime==as.character(pred_coex1Gen$Tu[x]) & Te_Regime==as.character(pred_coex1Gen$Te[x]) & Environment==as.character(pred_coex1Gen$Environment[x]))
  aux_lambdas<-subset(param_all_REP_lower, Tu_Regime==as.character(pred_coex1Gen$Tu[x]) & Te_Regime==as.character(pred_coex1Gen$Te[x]) & Environment==as.character(pred_coex1Gen$Environment[x]))

  bl<-aux_lambdas$Te_lambda[1]*10*exp(-aux_alphas$Te_intra[1]*10- aux_alphas$Te_inter[1]*10)
  
  bl
  })

pred_coex1Gen$Control_lambdaTu_L<-sapply(c(1:dim(pred_coex1Gen)[1]), function(x){
  cont<-subset(pred_coex1Gen, Environment==pred_coex1Gen$Environment[x] & Tu=="SR1")
  
  pred_coex1Gen$predTu_onlyLambda_L[x]/cont$predTu_onlyLambda_L[1]
  
})

pred_coex1Gen$Control_lambdaTe_L<-sapply(c(1:dim(pred_coex1Gen)[1]), function(x){
  cont<-subset(pred_coex1Gen, Environment==pred_coex1Gen$Environment[x] & Te=="SR4")
  
  pred_coex1Gen$predTe_onlyLambda_L[x]/cont$predTe_onlyLambda_L[1]
  
})

pred_coex1Gen$Control_lambdaIntraTu_L<-sapply(c(1:dim(pred_coex1Gen)[1]), function(x){
  cont<-subset(pred_coex1Gen, Environment==pred_coex1Gen$Environment[x] & Te=="SR4" & Tu=="SR1")
  
  pred_coex1Gen$predTu_Lambda_INTRA_L[x]/cont$predTu_Lambda_INTRA_L[1]
  
})

pred_coex1Gen$Control_lambdaIntraTe_L<-sapply(c(1:dim(pred_coex1Gen)[1]), function(x){
  cont<-subset(pred_coex1Gen, Environment==pred_coex1Gen$Environment[x] & Te=="SR4" & Tu=="SR1")
  
  pred_coex1Gen$predTe_Lambda_INTRA_L[x]/cont$predTe_Lambda_INTRA_L[1]
  
})

pred_coex1Gen$Control_ALLTu_L<-sapply(c(1:dim(pred_coex1Gen)[1]), function(x){
  cont<-subset(pred_coex1Gen, Environment==pred_coex1Gen$Environment[x] & Te=="SR4" & Tu=="SR1")
  
  pred_coex1Gen$predTu_ALL_L[x]/cont$predTu_ALL_L[1]
  
})

pred_coex1Gen$Control_ALLTe_L<-sapply(c(1:dim(pred_coex1Gen)[1]), function(x){
  cont<-subset(pred_coex1Gen, Environment==pred_coex1Gen$Environment[x] & Te=="SR4" & Tu=="SR1")
  
  pred_coex1Gen$predTe_ALL_L[x]/cont$predTe_ALL_L[1]
  
})

Upper

pred_coex1Gen$predTu_onlyLambda_U<-sapply(c(1:length(pred_coex1Gen$Tu)), function(x){
  aux_alphas<-subset(param_all_REP_upper, Tu_Regime==as.character(pred_coex1Gen$Tu[x]) & Te_Regime==as.character(pred_coex1Gen$Te[x]) & Environment==as.character(pred_coex1Gen$Environment[x]))

  bl<-aux_alphas$Tu_lambda[1]*10
  
  bl
  })

pred_coex1Gen$predTu_lambda_INTRA_U<-sapply(c(1:length(pred_coex1Gen$Tu)), function(x){
  aux_alphas<-subset(param_all_REP_lower, Tu_Regime==as.character(pred_coex1Gen$Tu[x]) & Te_Regime==as.character(pred_coex1Gen$Te[x]) & Environment==as.character(pred_coex1Gen$Environment[x]))
  aux_Lambdas<-subset(param_all_REP_upper, Tu_Regime==as.character(pred_coex1Gen$Tu[x]) & Te_Regime==as.character(pred_coex1Gen$Te[x]) & Environment==as.character(pred_coex1Gen$Environment[x]))

  bl<-aux_Lambdas$Tu_lambda[1]*10*exp(-aux_alphas$Tu_intra[1]*10)
  
  bl
  })

pred_coex1Gen$predTu_ALL_U<-sapply(c(1:length(pred_coex1Gen$Tu)), function(x){
  aux_alphas<-subset(param_all_REP_lower, Tu_Regime==as.character(pred_coex1Gen$Tu[x]) & Te_Regime==as.character(pred_coex1Gen$Te[x]) & Environment==as.character(pred_coex1Gen$Environment[x]))
  aux_Lambdas<-subset(param_all_REP_upper, Tu_Regime==as.character(pred_coex1Gen$Tu[x]) & Te_Regime==as.character(pred_coex1Gen$Te[x]) & Environment==as.character(pred_coex1Gen$Environment[x]))

  bl<-aux_Lambdas$Tu_lambda[1]*10*exp(-aux_alphas$Tu_intra[1]*10- aux_alphas$Tu_inter[1]*10)
  
  bl
  })


pred_coex1Gen$predTe_onlyLambda_U<-sapply(c(1:length(pred_coex1Gen$Tu)), function(x){
  aux_alphas<-subset(param_all_REP_upper, Tu_Regime==as.character(pred_coex1Gen$Tu[x]) & Te_Regime==as.character(pred_coex1Gen$Te[x]) & Environment==as.character(pred_coex1Gen$Environment[x]))

  bl<-aux_alphas$Te_lambda[1]*10
  
  bl
  })

pred_coex1Gen$predTe_lambda_INTRA_U<-sapply(c(1:length(pred_coex1Gen$Tu)), function(x){
  aux_alphas<-subset(param_all_REP_lower, Tu_Regime==as.character(pred_coex1Gen$Tu[x]) & Te_Regime==as.character(pred_coex1Gen$Te[x]) & Environment==as.character(pred_coex1Gen$Environment[x]))
  aux_Lambdas<-subset(param_all_REP_upper, Tu_Regime==as.character(pred_coex1Gen$Tu[x]) & Te_Regime==as.character(pred_coex1Gen$Te[x]) & Environment==as.character(pred_coex1Gen$Environment[x]))

  bl<-aux_Lambdas$Te_lambda[1]*10*exp(-aux_alphas$Te_intra[1]*10)
  
  bl
  })

pred_coex1Gen$predTe_ALL_U<-sapply(c(1:length(pred_coex1Gen$Tu)), function(x){
  aux_alphas<-subset(param_all_REP_lower, Tu_Regime==as.character(pred_coex1Gen$Tu[x]) & Te_Regime==as.character(pred_coex1Gen$Te[x]) & Environment==as.character(pred_coex1Gen$Environment[x]))
  aux_Lambdas<-subset(param_all_REP_upper, Tu_Regime==as.character(pred_coex1Gen$Tu[x]) & Te_Regime==as.character(pred_coex1Gen$Te[x]) & Environment==as.character(pred_coex1Gen$Environment[x]))

  bl<-aux_Lambdas$Te_lambda[1]*10*exp(-aux_alphas$Te_intra[1]*10- aux_alphas$Te_inter[1]*10)
  
  bl
  })

pred_coex1Gen$Control_LambdaTu_U<-sapply(c(1:dim(pred_coex1Gen)[1]), function(x){
  cont<-subset(pred_coex1Gen, Environment==pred_coex1Gen$Environment[x] & Tu=="SR1")
  
  pred_coex1Gen$predTu_onlyLambda_U[x]/cont$predTu_onlyLambda_U[1]
  
})

pred_coex1Gen$Control_LambdaTe_U<-sapply(c(1:dim(pred_coex1Gen)[1]), function(x){
  cont<-subset(pred_coex1Gen, Environment==pred_coex1Gen$Environment[x] & Te=="SR4")
  
  pred_coex1Gen$predTe_onlyLambda_U[x]/cont$predTe_onlyLambda_U[1]
  
})

pred_coex1Gen$Control_LambdaIntraTu_U<-sapply(c(1:dim(pred_coex1Gen)[1]), function(x){
  cont<-subset(pred_coex1Gen, Environment==pred_coex1Gen$Environment[x] & Te=="SR4" & Tu=="SR1")
  
  pred_coex1Gen$predTu_lambda_INTRA_U[x]/cont$predTu_lambda_INTRA_U[1]
  
})

pred_coex1Gen$Control_LambdaIntraTe_U<-sapply(c(1:dim(pred_coex1Gen)[1]), function(x){
  cont<-subset(pred_coex1Gen, Environment==pred_coex1Gen$Environment[x] & Te=="SR4" & Tu=="SR1")
  
  pred_coex1Gen$predTe_lambda_INTRA_U[x]/cont$predTe_lambda_INTRA_U[1]
  
})

pred_coex1Gen$Control_ALLTu_U<-sapply(c(1:dim(pred_coex1Gen)[1]), function(x){
  cont<-subset(pred_coex1Gen, Environment==pred_coex1Gen$Environment[x] & Te=="SR4" & Tu=="SR1")
  
  pred_coex1Gen$predTu_ALL_U[x]/cont$predTu_ALL_U[1]
  
})

pred_coex1Gen$Control_ALLTe_U<-sapply(c(1:dim(pred_coex1Gen)[1]), function(x){
  cont<-subset(pred_coex1Gen, Environment==pred_coex1Gen$Environment[x] & Te=="SR4" & Tu=="SR1")
  
  pred_coex1Gen$predTe_ALL_U[x]/cont$predTe_ALL_U[1]
  
})

pred_coex1Gen[,c("predTu_ALL", "predTu_ALL_U", "predTu_onlyLambda", "predTu_onlyLambda_U", "predTu_Lambda_INTRA", "predTu_lambda_INTRA_U")]
##   predTu_ALL predTu_ALL_U predTu_onlyLambda predTu_onlyLambda_U
## 1  12.473836     17.13965          24.82408            26.50963
## 2   9.916002     11.48540          12.20772            12.61243
## 3  12.834762     18.32623          25.47805            27.32934
## 4  10.691389     13.13282          14.02913            14.64993
## 5  13.739945     18.76665          24.82408            26.50963
## 6  11.180061     13.07897          12.20772            12.61243
## 7  17.080018     24.17479          25.47805            27.32934
## 8  11.439811     14.30747          14.02913            14.64993
##   predTu_Lambda_INTRA predTu_lambda_INTRA_U
## 1            18.57041              22.36856
## 2            11.08162              12.05820
## 3            19.52653              23.98961
## 4            12.36345              13.90353
## 5            18.57041              22.36856
## 6            11.08162              12.05820
## 7            19.52653              23.98961
## 8            12.36345              13.90353

reshaping

pred_coex1Gen_long<-gather(pred_coex1Gen[,c("Te","Tu","Environment","Control_lambdaTe" , "Control_lambdaTu","Control_lambdaIntraTe", "Control_lambdaIntraTu","Control_ALLTe" ,"Control_ALLTu",  "predTe_onlyLambda","predTe_Lambda_INTRA" ,"predTe_ALL" ,"predTu_onlyLambda","predTu_Lambda_INTRA","predTu_ALL" )], parameter, value, c("Control_lambdaTe" , "Control_lambdaTu","Control_lambdaIntraTe", "Control_lambdaIntraTu","Control_ALLTe" ,"Control_ALLTu",  "predTe_onlyLambda","predTe_Lambda_INTRA" ,"predTe_ALL" ,"predTu_onlyLambda","predTu_Lambda_INTRA","predTu_ALL" ))

pred_coex1Gen_long_L<-gather(pred_coex1Gen[,c("Te","Tu","Environment","Control_lambdaTe_L" , "Control_lambdaTu_L","Control_lambdaIntraTe_L", "Control_lambdaIntraTu_L","Control_ALLTe_L" ,"Control_ALLTu_L",  "predTe_onlyLambda_L","predTe_Lambda_INTRA_L" ,"predTe_ALL_L" ,"predTu_onlyLambda_L","predTu_Lambda_INTRA_L","predTu_ALL_L" )], parameter, value_L, c("Control_lambdaTe_L" , "Control_lambdaTu_L","Control_lambdaIntraTe_L", "Control_lambdaIntraTu_L","Control_ALLTe_L" ,"Control_ALLTu_L",  "predTe_onlyLambda_L","predTe_Lambda_INTRA_L" ,"predTe_ALL_L" ,"predTu_onlyLambda_L","predTu_Lambda_INTRA_L","predTu_ALL_L"))

pred_coex1Gen_long_L$parameter2<-mapvalues(pred_coex1Gen_long_L$parameter,c("Control_lambdaTe_L" , "Control_lambdaTu_L","Control_lambdaIntraTe_L", "Control_lambdaIntraTu_L","Control_ALLTe_L" ,"Control_ALLTu_L",  "predTe_onlyLambda_L","predTe_Lambda_INTRA_L" ,"predTe_ALL_L" ,"predTu_onlyLambda_L","predTu_Lambda_INTRA_L","predTu_ALL_L"), c("Control_lambdaTe" , "Control_lambdaTu","Control_lambdaIntraTe", "Control_lambdaIntraTu","Control_ALLTe" ,"Control_ALLTu",  "predTe_onlyLambda","predTe_Lambda_INTRA" ,"predTe_ALL" ,"predTu_onlyLambda","predTu_Lambda_INTRA","predTu_ALL") )


pred_coex1Gen_long_U<-gather(pred_coex1Gen[,c("Te","Tu","Environment","Control_LambdaTe_U" , "Control_LambdaTu_U","Control_LambdaIntraTe_U", "Control_LambdaIntraTu_U","Control_ALLTe_U" ,"Control_ALLTu_U",  "predTe_onlyLambda_U","predTe_lambda_INTRA_U" ,"predTe_ALL_U" ,"predTu_onlyLambda_U","predTu_lambda_INTRA_U","predTu_ALL_U" )], parameter, value_U, c("Control_LambdaTe_U" , "Control_LambdaTu_U","Control_LambdaIntraTe_U", "Control_LambdaIntraTu_U","Control_ALLTe_U" ,"Control_ALLTu_U",  "predTe_onlyLambda_U","predTe_lambda_INTRA_U" ,"predTe_ALL_U" ,"predTu_onlyLambda_U","predTu_lambda_INTRA_U","predTu_ALL_U") )

pred_coex1Gen_long_U$parameter2<-mapvalues(pred_coex1Gen_long_U$parameter,c("Control_LambdaTe_U" , "Control_LambdaTu_U","Control_LambdaIntraTe_U", "Control_LambdaIntraTu_U","Control_ALLTe_U" ,"Control_ALLTu_U",  "predTe_onlyLambda_U","predTe_lambda_INTRA_U" ,"predTe_ALL_U" ,"predTu_onlyLambda_U","predTu_lambda_INTRA_U","predTu_ALL_U"), c("Control_lambdaTe" , "Control_lambdaTu","Control_lambdaIntraTe", "Control_lambdaIntraTu","Control_ALLTe" ,"Control_ALLTu",  "predTe_onlyLambda","predTe_Lambda_INTRA" ,"predTe_ALL" ,"predTu_onlyLambda","predTu_Lambda_INTRA","predTu_ALL") )

pred_coex1Gen_long$parameter2<-pred_coex1Gen_long$parameter

pred_coex1Gen_long<-left_join(pred_coex1Gen_long, pred_coex1Gen_long_L, by=c("Te","Tu", "parameter2","Environment"))

pred_coex1Gen_long<-left_join(pred_coex1Gen_long, pred_coex1Gen_long_U, by=c("Te","Tu", "parameter2","Environment"))

colnames(pred_coex1Gen_long)<-c("Te", "Tu", "Environment", "parameter", "value", "parameter2","parameter_L", "value_L", "parameter_U", "value_U" )

pred_coex1Gen_long$parameter3<-factor(pred_coex1Gen_long$parameter, c("Control_lambdaTe" , "Control_lambdaTu","Control_lambdaIntraTe", "Control_lambdaIntraTu","Control_ALLTe" ,"Control_ALLTu",  "predTe_onlyLambda","predTe_Lambda_INTRA" ,"predTe_ALL" ,"predTu_onlyLambda","predTu_Lambda_INTRA","predTu_ALL"))
str(pred_coex1Gen)
## 'data.frame':    8 obs. of  39 variables:
##  $ Te                     : chr  "SR4" "SR4" "SR4" "SR4" ...
##  $ Tu                     : chr  "SR1" "SR1" "SR2" "SR2" ...
##  $ Environment            : chr  "N" "Cd" "N" "Cd" ...
##  $ predTu_onlyLambda      : num  24.8 12.2 25.5 14 24.8 ...
##  $ predTu_Lambda_INTRA    : num  18.6 11.1 19.5 12.4 18.6 ...
##  $ predTu_ALL             : num  12.47 9.92 12.83 10.69 13.74 ...
##  $ predTe_onlyLambda      : num  55.4 18 55.4 18 44.3 ...
##  $ predTe_Lambda_INTRA    : num  45.6 16.3 45.6 16.3 41 ...
##  $ predTe_ALL             : num  19.6 17.5 27.4 16.8 20 ...
##  $ Control_lambdaTu       : num  1 1 1.03 1.15 1 ...
##  $ Control_lambdaTe       : num  1 1 1 1 0.8 ...
##  $ Control_lambdaIntraTu  : num  1 1 1.05 1.12 1 ...
##  $ Control_lambdaIntraTe  : num  1 1 1 1 0.899 ...
##  $ Control_ALLTu          : num  1 1 1.03 1.08 1.1 ...
##  $ Control_ALLTe          : num  1 1 1.4 0.96 1.02 ...
##  $ predTu_onlyLambda_L    : num  23.1 11.8 23.6 13.4 23.1 ...
##  $ predTu_Lambda_INTRA_L  : num  15.3 10.2 15.8 11 15.3 ...
##  $ predTu_ALL_L           : num  9.04 8.55 8.94 8.69 10.01 ...
##  $ predTe_onlyLambda_L    : num  49 16.9 49 16.9 39.2 ...
##  $ predTe_Lambda_INTRA_L  : num  31.4 13.8 31.4 13.8 29.1 ...
##  $ predTe_ALL_L           : num  11 13 14.9 12.3 11.4 ...
##  $ Control_lambdaTu_L     : num  1 1 1.02 1.14 1 ...
##  $ Control_lambdaTe_L     : num  1 1 1 1 0.8 ...
##  $ Control_lambdaIntraTu_L: num  1 1 1.03 1.08 1 ...
##  $ Control_lambdaIntraTe_L: num  1 1 1 1 0.926 ...
##  $ Control_ALLTu_L        : num  1 1 0.989 1.016 1.108 ...
##  $ Control_ALLTe_L        : num  1 1 1.351 0.952 1.033 ...
##  $ predTu_onlyLambda_U    : num  26.5 12.6 27.3 14.6 26.5 ...
##  $ predTu_lambda_INTRA_U  : num  22.4 12.1 24 13.9 22.4 ...
##  $ predTu_ALL_U           : num  17.1 11.5 18.3 13.1 18.8 ...
##  $ predTe_onlyLambda_U    : num  61.8 19 61.8 19 49.4 ...
##  $ predTe_lambda_INTRA_U  : num  65.5 19 65.5 19 57.2 ...
##  $ predTe_ALL_U           : num  34.3 23.6 49.7 22.9 34.9 ...
##  $ Control_LambdaTu_U     : num  1 1 1.03 1.16 1 ...
##  $ Control_LambdaTe_U     : num  1 1 1 1 0.799 ...
##  $ Control_LambdaIntraTu_U: num  1 1 1.07 1.15 1 ...
##  $ Control_LambdaIntraTe_U: num  1 1 1 1 0.873 ...
##  $ Control_ALLTu_U        : num  1 1 1.07 1.14 1.09 ...
##  $ Control_ALLTe_U        : num  1 1 1.447 0.969 1.017 ...

Figure1

ggplot(subset(pred_coex1Gen_long, parameter=="predTe_onlyLambda" |  parameter=="predTe_Lambda_INTRA" |  parameter=="predTe_ALL"), aes(y=parameter3, x=value))+
    facet_grid(.~Environment, labeller=labeller(Environment=Env))+
  geom_errorbarh(aes(xmin=value_L, xmax=value_U, group=interaction(Te, Tu)), colour="black", height=0.5, position=position_dodge2(0.5))+
  geom_point(aes(fill=interaction(Te, Tu)),size=2.5, position=position_dodge2(0.5), stat="identity", shape=21)+
  geom_vline(xintercept = 1, colour="lightgray", linetype="dashed")+
  theme_bw()+
    theme_ines+
  scale_fill_brewer(palette = "Spectral", labels=c("Te no cadmium:Tu no cadmium", "Te cadmium:Tu no cadmium", "Te no cadmium:Tu cadmium", "Te cadmium:Tu cadmium"), name="")+
  guides(fill=guide_legend(nrow=2))+
  xlab(expression(paste("Predicted offspring production for ", italic("T. evansi"))))+
  scale_y_discrete(labels=c(expression(lambda+ alpha[ii] + alpha [ij]),expression(lambda+ alpha[ii]), expression(lambda)), limits=rev(levels(droplevels(subset(pred_coex1Gen_long, parameter=="predTe_onlyLambda" |  parameter=="predTe_Lambda_INTRA" |  parameter=="predTe_ALL"))$parameter3)))+
  theme(legend.position = "bottom", axis.text = element_text(size=12), axis.title = element_text(face="plain", size=12))+
  ylab("")

save_plot("./Analyses/cxr_normal_REP/Fig1A.pdf", width=17.5, height=10)



ggplot(subset(pred_coex1Gen_long, parameter=="predTu_onlyLambda" |  parameter=="predTu_Lambda_INTRA" |  parameter=="predTu_ALL"), aes(y=parameter3, x=value))+
    facet_grid(.~Environment, labeller=labeller(Environment=Env))+
  geom_errorbarh(aes(xmin=value_L, xmax=value_U, group=interaction(Te, Tu)), colour="black", height=0.5, position=position_dodge2(0.5))+
  geom_point(aes(fill=interaction(Te, Tu)),size=2.5, position=position_dodge2(0.5), stat="identity", shape=21)+
  geom_vline(xintercept = 1, colour="lightgray", linetype="dashed")+
  theme_bw()+
    theme_ines+
  scale_fill_brewer(palette = "Spectral", labels=c("Te no cadmium:Tu no cadmium", "Te cadmium:Tu no cadmium", "Te no cadmium:Tu cadmium", "Te cadmium:Tu cadmium"), name="")+
  xlab(expression(paste("Predicted offspring production for ", italic("T. urticae"))))+
  guides(fill=guide_legend(nrow=2))+
  scale_y_discrete(labels=c(expression(lambda+ alpha[ii] + alpha [ij]),expression(lambda+ alpha[ii]), expression(lambda)), limits=rev(levels(droplevels(subset(pred_coex1Gen_long, parameter=="predTu_onlyLambda" |  parameter=="predTu_Lambda_INTRA" |  parameter=="predTu_ALL"))$parameter3)))+
  theme(legend.position = "bottom", axis.text = element_text(size=12), axis.title = element_text(face="plain", size=12))+
  ylab("")

save_plot("./Analyses/cxr_normal_REP/Fig1B.pdf", width=17.5, height=10)

6 - Bootstrap differences between selection regimes

For each question we will randomize the replicates between selection regimes.

6.1 - Does cadmium change parameters?

nboot<-1000

#Bootstrap to reestimate the p-value obtained for growth rate and intraspecific competition.
boot_tu_gr_intra_env<-as.data.frame(t(sapply(c(1:nboot),function(x){
  
  if(x%%10 ==0){
    print(x)
  }
  
  auxi<-subset(param_all_w0, Tu_Regime=="SR1" & Te_Regime=="SR4" )
  rand_numb<-sample(c(1:dim(auxi)[1]), dim(auxi)[1], replace = TRUE)
  auxi$Tu_lambda<-auxi[rand_numb,"Tu_lambda"] # randomizing the trais
  auxi$Tu_intra<-auxi[rand_numb,"Tu_intra"]
  auxi$Tu_inter<-auxi[rand_numb,"Tu_inter"]
  
  gr <-glmmTMB(Tu_lambda~Environment, data=auxi, family=Gamma(link="log"))
  intra <-glmmTMB(Tu_intra~Environment, data=auxi)
  inter<-glmmTMB(Tu_inter~Environment, data=auxi)
  
  sum_auxi<-auxi %>% group_by(Environment)%>% summarize(meanGr=mean(Tu_lambda, na.rm=TRUE), meanIntra=mean(Tu_intra, na.rm=TRUE), meaninter=mean(Tu_inter, na.rm=TRUE)) %>% as.data.frame()
  
  # N - Cd
  diff<-sum_auxi[2,c(2:4)]-sum_auxi[1,(2:4)]
  
  gr_p<-as.data.frame(Anova(gr))[1,3]
  intra_p<-as.data.frame(Anova(intra))[1,3]
  inter_p<-as.data.frame(Anova(inter))[1,3]
  
  c(gr_p, intra_p, inter_p, diff[1,1], diff[1,2], diff[1,3])
  
} )))


boot_te_gr_intra_env<-as.data.frame(t(sapply(c(1:nboot),function(x){
  
  if(x%%10 ==0){
    print(x)
  }
  
  auxi<-subset(param_all_w0, Tu_Regime=="SR1" & Te_Regime=="SR4" )
  rand_numb<-sample(c(1:dim(auxi)[1]), dim(auxi)[1], replace = TRUE)
  auxi$Te_lambda<-auxi[rand_numb,"Te_lambda"] # randomizing the trais
  auxi$Te_intra<-auxi[rand_numb,"Te_intra"]
  auxi$Te_inter<-auxi[rand_numb,"Te_inter"]
  
  gr <-glmmTMB(Te_lambda~Environment, data=auxi, family=Gamma(link="log"))
  intra <-glmmTMB(Te_intra~Environment, data=auxi)
  inter <-glmmTMB(Te_inter~Environment, data=auxi)
  
  sum_auxi<-auxi %>% group_by(Environment)%>% summarize(meanGr=mean(Te_lambda, na.rm=TRUE), meanIntra=mean(Te_intra, na.rm=TRUE), meaninter=mean(Te_inter, na.rm=TRUE)) %>% as.data.frame()
  
  # N - Cd
  diff<-sum_auxi[2,c(2:4)]-sum_auxi[1,(2:4)]
  
  gr_p<-as.data.frame(Anova(gr))[1,3]
  intra_p<-as.data.frame(Anova(intra))[1,3]
  inter_p<-as.data.frame(Anova(inter))[1,3]
  
  c(gr_p, intra_p, inter_p,diff[1,1], diff[1,2], diff[1,3])
  
} )))
colnames(boot_tu_gr_intra_env)<-c("lambda_p","intra_p","inter_p", "lambda_diff", "intra_diff", "inter_diff")
colnames(boot_te_gr_intra_env)<-c("lambda_p","intra_p","inter_p", "lambda_diff", "intra_diff", "inter_diff")
str(boot_te_gr_intra_env)

ggplot(boot_tu_gr_intra_env, aes(x=lambda_p))+
geom_histogram()+
geom_vline(data=as.data.frame(Anova(gr_tu_cd_2)), aes_string(xintercept=as.data.frame(Anova(gr_tu_cd_2))[,3]))


print("Boot p-values for tests between environments")
length(which(boot_tu_gr_intra_env$lambda_p<=as.data.frame(Anova(gr_tu_cd_2))[,3]))/(nboot+1)

length(which(boot_tu_gr_intra_env$intra_p<=as.data.frame(Anova(intra_tu_cd_1))[,3]))/(nboot+1)

length(which(boot_tu_gr_intra_env$inter_p<=as.data.frame(Anova(inter_tu_cd_1))[,3]))/(nboot+1)

length(which(boot_te_gr_intra_env$lambda_p<=as.data.frame(Anova(gr_te_cd_2))[,3]))/(nboot+1)

length(which(boot_te_gr_intra_env$intra_p<=as.data.frame(Anova(intra_te_cd_1))[,3]))/(nboot+1)

length(which(boot_te_gr_intra_env$inter_p<=as.data.frame(Anova(inter_te_cd_1))[,3]))/(nboot+1)

as.data.frame(Anova(gr_tu_cd_2))[,3]
as.data.frame(Anova(intra_tu_cd_1))[,3]
as.data.frame(Anova(inter_tu_cd_1))[,3]
as.data.frame(Anova(gr_te_cd_2))[,3]
as.data.frame(Anova(intra_te_cd_1))[,3]
as.data.frame(Anova(inter_te_cd_1))[,3]


length(which(boot_tu_gr_intra_env$lambda_p<=0.05))/(nboot)

length(which(boot_tu_gr_intra_env$intra_p<=0.05))/(nboot)

length(which(boot_tu_gr_intra_env$inter_p<=0.05))/(nboot)

length(which(boot_te_gr_intra_env$lambda_p<=0.05))/(nboot)

length(which(boot_te_gr_intra_env$intra_p<=0.05))/(nboot)

length(which(boot_te_gr_intra_env$inter_p<=0.05))/(nboot)

6.2 - Does evolution change the performance in cadmium?

#Bootstrap to reestimate the p-value obtained for growth rate and intraspecific competition.
boot_tu_evolcd<-as.data.frame(t(sapply(c(1:nboot),function(x){
  
  if(x%%10 ==0){
    print(x)
  }
  
  auxi<-subset(param_all_w0, Environment=="Cd"& Te_Regime=="SR4")
  rand_numb<-sample(c(1:dim(auxi)[1]), dim(auxi)[1], replace = TRUE)
  auxi$Tu_lambda<-auxi[rand_numb,"Tu_lambda"] # randomizing the trais
  auxi$Tu_intra<-auxi[rand_numb,"Tu_intra"]
  
  auxi2<-subset(param_all_w0, Environment=="Cd")
  rand_numb2<-sample(c(1:dim(auxi2)[1]), dim(auxi2)[1], replace = TRUE)
  auxi2$Tu_inter<-auxi2[rand_numb2,"Tu_inter"]
  
  gr <-glmmTMB(Tu_lambda~Tu_Regime, data=auxi, family=Gamma(link="log"))
  intra <-glmmTMB(Tu_intra~Tu_Regime, data=auxi)
  inter<-glmmTMB(Tu_inter~Tu_Regime*Te_Regime, data=auxi2)
  
  #inter<-glmmTMB(Tu_inter~Environment, data=auxi)
  
  sum_auxi<-auxi %>% group_by(Tu_Regime)%>% summarize(meanGr=mean(Tu_lambda, na.rm=TRUE), meanIntra=mean(Tu_intra, na.rm=TRUE)) %>% as.data.frame()
  
   sum_auxi2<-auxi2 %>% group_by(Tu_Regime, Te_Regime)%>% summarize( meanInter=mean(Tu_inter, na.rm=TRUE)) %>% as.data.frame()
  
  # N - Cd
  diff<-sum_auxi[2,c(2:3)]-sum_auxi[1,(2:3)]
  diff2<-sum_auxi2[1,3]-sum_auxi2[2,3] # Evolution of the competitor with control focal
  diff3<-sum_auxi2[1,3]-sum_auxi2[3,3] # Evolution of the focal with control competitor
  diff4<-sum_auxi2[2,3]-sum_auxi2[4,3] # Evolution of the focal with evolved competitor
  diff5<-sum_auxi2[3,3]-sum_auxi2[4,3] # Evolution of the competitor with evolved focal
  
  gr_p<-as.data.frame(Anova(gr))[1,3]
  intra_p<-as.data.frame(Anova(intra))[1,3]
  inter_p<-as.data.frame(Anova(inter))[1,3]
  inter_p2<-as.data.frame(Anova(inter))[2,3]
  inter_p3<-as.data.frame(Anova(inter))[3,3]
  
  c(gr_p, intra_p, inter_p,inter_p2, inter_p3, diff[1,1], diff[1,2], diff2, diff3, diff4,diff5)
  
} )))


boot_te_evolcd<-as.data.frame(t(sapply(c(1:nboot),function(x){
  
  if(x%%10 ==0){
    print(x)
  }
  
  auxi<-subset(param_all_w0, Environment=="Cd"& Tu_Regime=="SR1")
  rand_numb<-sample(c(1:dim(auxi)[1]), dim(auxi)[1], replace = TRUE)
  auxi$Te_lambda<-auxi[rand_numb,"Te_lambda"] # randomizing the trais
  auxi$Te_intra<-auxi[rand_numb,"Te_intra"]
  
 # print(x)
  
  auxi2<-subset(param_all_w0, Environment=="Cd")
  rand_numb2<-sample(c(1:dim(auxi2)[1]), dim(auxi2)[1], replace = TRUE)
  auxi2$Te_inter<-auxi2[rand_numb2,"Te_inter"]
  
  gr <-glmmTMB(Te_lambda~Te_Regime, data=auxi, family=Gamma(link="log"))
  intra <-glmmTMB(Te_intra~Te_Regime, data=auxi)
  inter<-glmmTMB(Te_inter~Tu_Regime*Te_Regime, data=auxi2)
  
  #inter<-glmmTMB(Tu_inter~Environment, data=auxi)
  
  sum_auxi<-auxi %>% group_by(Te_Regime)%>% summarize(meanGr=mean(Te_lambda, na.rm=TRUE), meanIntra=mean(Te_intra, na.rm=TRUE)) %>% as.data.frame()
  
   sum_auxi2<-auxi2 %>% group_by(Tu_Regime, Te_Regime)%>% summarize( meanInter=mean(Te_inter, na.rm=TRUE)) %>% as.data.frame()
  
  # N - Cd
  diff<-sum_auxi[2,c(2:3)]-sum_auxi[1,(2:3)]
  diff2<-sum_auxi2[1,3]-sum_auxi2[2,3] # Evolution of the competitor with control focal
  diff3<-sum_auxi2[1,3]-sum_auxi2[3,3] # Evolution of the focal with control competitor
  diff4<-sum_auxi2[2,3]-sum_auxi2[4,3] # Evolution of the focal with evolved competitor
  diff5<-sum_auxi2[3,3]-sum_auxi2[4,3] # Evolution of the competitor with evolved focal
  
  gr_p<-as.data.frame(Anova(gr))[1,3]
  intra_p<-as.data.frame(Anova(intra))[1,3]
  inter_p<-as.data.frame(Anova(inter))[1,3]
  inter_p2<-as.data.frame(Anova(inter))[2,3]
  inter_p3<-as.data.frame(Anova(inter))[3,3]
  
  c(gr_p, intra_p, inter_p,inter_p2, inter_p3, diff[1,1], diff[1,2], diff2, diff3, diff4,diff5)
  
} )))


colnames(boot_tu_evolcd)<-c("lambda_p","intra_p","inter_p_TuReg","inter_p_TeReg","inter_p_int", "lambda_diff", "intra_diff", "inter_diffEvolComp_focalControl","inter_diffEvolFocal_CompControl","inter_diffEvolFocal_EvolComp","inter_diffEvolComp_focalEvol" )
colnames(boot_te_evolcd)<-c("lambda_p","intra_p","inter_p_TuReg","inter_p_TeReg","inter_p_int", "lambda_diff", "intra_diff", "inter_diffEvolComp_focalControl","inter_diffEvolFocal_CompControl","inter_diffEvolFocal_EvolComp","inter_diffEvolComp_focalEvol" )

print("Boot p-values for tests for evolution in cadmium")
length(which(boot_tu_evolcd$lambda_p<=as.data.frame(Anova(gr_tu_ev_2))[,3]))/(nboot+1)

length(which(boot_tu_evolcd$intra_p<=as.data.frame(Anova(intra_tu_ev_1))[,3]))/(nboot+1)

length(which(boot_tu_evolcd$inter_p_TuReg<=as.data.frame(Anova(inter_tu_ev_1))[1,3]))/(nboot+1)

length(which(boot_tu_evolcd$inter_p_TeReg<=as.data.frame(Anova(inter_tu_ev_1))[2,3]))/(nboot+1)

length(which(boot_tu_evolcd$inter_p_int<=as.data.frame(Anova(inter_tu_ev_1))[3,3]))/(nboot+1)

length(which(boot_te_evolcd$lambda_p<=as.data.frame(Anova(gr_te_ev_2))[,3]))/(nboot+1)

length(which(boot_te_evolcd$intra_p<=as.data.frame(Anova(intra_te_ev_1))[,3]))/(nboot+1)

length(which(boot_te_evolcd$inter_p_TuReg<=as.data.frame(Anova(inter_te_ev_1))[1,3]))/(nboot+1)

length(which(boot_te_evolcd$inter_p_TeReg<=as.data.frame(Anova(inter_te_ev_1))[2,3]))/(nboot+1)

length(which(boot_te_evolcd$inter_p_int<=as.data.frame(Anova(inter_te_ev_1))[3,3]))/(nboot+1)

hist(boot_tu_evolcd$lambda_p)
abline(v=as.data.frame(Anova(gr_tu_ev_2))[,3], col="red")

hist(boot_tu_evolcd$intra_p)
abline(v=as.data.frame(Anova(intra_tu_ev_1))[,3], col="red")

hist(boot_tu_evolcd$inter_p_TuReg)
abline(v=as.data.frame(Anova(inter_tu_ev_1))[1,3], col="red")

hist(boot_tu_evolcd$inter_p_TeReg)
abline(v=as.data.frame(Anova(inter_tu_ev_1))[2,3], col="red")

hist(boot_tu_evolcd$inter_p_int)
abline(v=as.data.frame(Anova(inter_tu_ev_1))[3,3], col="red")


hist(boot_te_evolcd$lambda_p)
abline(v=as.data.frame(Anova(gr_te_ev_2))[,3], col="red")

hist(boot_te_evolcd$intra_p)
abline(v=as.data.frame(Anova(intra_te_ev_1))[,3], col="red")

hist(boot_te_evolcd$inter_p_TuReg)
abline(v=as.data.frame(Anova(inter_te_ev_1))[1,3], col="red")

hist(boot_te_evolcd$inter_p_TeReg)
abline(v=as.data.frame(Anova(inter_te_ev_1))[2,3], col="red")

hist(boot_te_evolcd$inter_p_int)
abline(v=as.data.frame(Anova(inter_te_ev_1))[3,3], col="red")




as.data.frame(Anova(gr_tu_ev_2))[,3]
as.data.frame(Anova(intra_tu_ev_1))[,3]
as.data.frame(Anova(inter_tu_ev_1))[1,3]
as.data.frame(Anova(inter_tu_ev_1))[2,3]
as.data.frame(Anova(inter_tu_ev_1))[3,3]
as.data.frame(Anova(gr_te_ev_2))[,3]
as.data.frame(Anova(intra_te_ev_1))[,3]
as.data.frame(Anova(inter_te_ev_1))[1,3]
as.data.frame(Anova(inter_te_ev_1))[2,3]
as.data.frame(Anova(inter_te_ev_1))[3,3]


#Number of times that p-value was lower than 0.05

length(which(boot_tu_evolcd$lambda_p<=0.05))/(nboot)
length(which(boot_tu_evolcd$intra_p<=0.05))/(nboot)
length(which(boot_tu_evolcd$inter_p_TuReg<=0.05))/(nboot)
length(which(boot_tu_evolcd$inter_p_TeReg<=0.05))/(nboot)
length(which(boot_tu_evolcd$inter_p_int<=0.05))/(nboot)
length(which(boot_te_evolcd$lambda_p<=0.05))/(nboot)
length(which(boot_te_evolcd$intra_p<=0.05))/(nboot)
length(which(boot_te_evolcd$inter_p_TuReg<=0.05))/(nboot)
length(which(boot_te_evolcd$inter_p_TeReg<=0.05))/(nboot)
length(which(boot_te_evolcd$inter_p_int<=0.05))/(nboot)

2.3.4 - Does evolution change the ancestral?

#Bootstrap to reestimate the p-value obtained for growth rate and intraspecific competition.
boot_tu_evolN<-as.data.frame(t(sapply(c(1:nboot),function(x){
  
  if(x%%10 ==0){
    print(x)
  }
  
  auxi<-subset(param_all_w0, Environment=="N"& Te_Regime=="SR4")
  rand_numb<-sample(c(1:dim(auxi)[1]), dim(auxi)[1], replace = TRUE)
  auxi$Tu_lambda<-auxi[rand_numb,"Tu_lambda"] # randomizing the trais
  auxi$Tu_intra<-auxi[rand_numb,"Tu_intra"]
  
  auxi2<-subset(param_all_w0, Environment=="N")
  rand_numb2<-sample(c(1:dim(auxi2)[1]), dim(auxi2)[1], replace = TRUE)
  auxi2$Tu_inter<-auxi2[rand_numb2,"Tu_inter"]
  
  gr <-glmmTMB(Tu_lambda~Tu_Regime, data=auxi, family=Gamma(link="log"))
  intra <-glmmTMB(Tu_intra~Tu_Regime, data=auxi)
  inter<-glmmTMB(Tu_inter~Tu_Regime*Te_Regime, data=auxi2)
  
  #inter<-glmmTMB(Tu_inter~Environment, data=auxi)
  
  sum_auxi<-auxi %>% group_by(Tu_Regime)%>% summarize(meanGr=mean(Tu_lambda, na.rm=TRUE), meanIntra=mean(Tu_intra, na.rm=TRUE)) %>% as.data.frame()
  
   sum_auxi2<-auxi2 %>% group_by(Tu_Regime, Te_Regime)%>% summarize( meanInter=mean(Tu_inter, na.rm=TRUE)) %>% as.data.frame()
  
  # N - N
  diff<-sum_auxi[2,c(2:3)]-sum_auxi[1,(2:3)]
  diff2<-sum_auxi2[1,3]-sum_auxi2[2,3] # Evolution of the competitor with control focal
  diff3<-sum_auxi2[1,3]-sum_auxi2[3,3] # Evolution of the focal with control competitor
  diff4<-sum_auxi2[2,3]-sum_auxi2[4,3] # Evolution of the focal with evolved competitor
  diff5<-sum_auxi2[3,3]-sum_auxi2[4,3] # Evolution of the competitor with evolved focal
  
  gr_p<-as.data.frame(Anova(gr))[1,3]
  intra_p<-as.data.frame(Anova(intra))[1,3]
  inter_p<-as.data.frame(Anova(inter))[1,3]
  inter_p2<-as.data.frame(Anova(inter))[2,3]
  inter_p3<-as.data.frame(Anova(inter))[3,3]
  
  c(gr_p, intra_p, inter_p,inter_p2, inter_p3, diff[1,1], diff[1,2], diff2, diff3, diff4,diff5)
  
} )))


boot_te_evolN<-as.data.frame(t(sapply(c(1:nboot),function(x){
  
  if(x%%10 ==0){
    print(x)
  }
  
  auxi<-subset(param_all_w0, Environment=="N"& Tu_Regime=="SR1")
  rand_numb<-sample(c(1:dim(auxi)[1]), dim(auxi)[1], replace = TRUE)
  auxi$Te_lambda<-auxi[rand_numb,"Te_lambda"] # randomizing the trais
  auxi$Te_intra<-auxi[rand_numb,"Te_intra"]
  
 # print(x)
  
  auxi2<-subset(param_all_w0, Environment=="N")
  rand_numb2<-sample(c(1:dim(auxi2)[1]), dim(auxi2)[1], replace = TRUE)
  auxi2$Te_inter<-auxi2[rand_numb2,"Te_inter"]
  
  gr <-glmmTMB(Te_lambda~Te_Regime, data=auxi, family=Gamma(link="log"))
  intra <-glmmTMB(Te_intra~Te_Regime, data=auxi)
  inter<-glmmTMB(Te_inter~Tu_Regime*Te_Regime, data=auxi2)
  
  #inter<-glmmTMB(Tu_inter~Environment, data=auxi)
  
  sum_auxi<-auxi %>% group_by(Te_Regime)%>% summarize(meanGr=mean(Te_lambda, na.rm=TRUE), meanIntra=mean(Te_intra, na.rm=TRUE)) %>% as.data.frame()
  
   sum_auxi2<-auxi2 %>% group_by(Tu_Regime, Te_Regime)%>% summarize( meanInter=mean(Te_inter, na.rm=TRUE)) %>% as.data.frame()
  
  # N - N
  diff<-sum_auxi[2,c(2:3)]-sum_auxi[1,(2:3)]
  diff2<-sum_auxi2[1,3]-sum_auxi2[2,3] # Evolution of the competitor with control focal
  diff3<-sum_auxi2[1,3]-sum_auxi2[3,3] # Evolution of the focal with control competitor
  diff4<-sum_auxi2[2,3]-sum_auxi2[4,3] # Evolution of the focal with evolved competitor
  diff5<-sum_auxi2[3,3]-sum_auxi2[4,3] # Evolution of the competitor with evolved focal
  
  gr_p<-as.data.frame(Anova(gr))[1,3]
  intra_p<-as.data.frame(Anova(intra))[1,3]
  inter_p<-as.data.frame(Anova(inter))[1,3]
  inter_p2<-as.data.frame(Anova(inter))[2,3]
  inter_p3<-as.data.frame(Anova(inter))[3,3]
  
  c(gr_p, intra_p, inter_p,inter_p2, inter_p3, diff[1,1], diff[1,2], diff2, diff3, diff4,diff5)
  
} )))


colnames(boot_tu_evolN)<-c("lambda_p","intra_p","inter_p_TuReg","inter_p_TeReg","inter_p_int", "lambda_diff", "intra_diff", "inter_diffEvolComp_focalControl","inter_diffEvolFocal_CompControl","inter_diffEvolFocal_EvolComp","inter_diffEvolComp_focalEvol" )
colnames(boot_te_evolN)<-c("lambda_p","intra_p","inter_p_TuReg","inter_p_TeReg","inter_p_int", "lambda_diff", "intra_diff", "inter_diffEvolComp_focalControl","inter_diffEvolFocal_CompControl","inter_diffEvolFocal_EvolComp","inter_diffEvolComp_focalEvol" )

print("Boot p-values for tests for evolution in cadmium")
length(which(boot_tu_evolN$lambda_p<=as.data.frame(Anova(gr_tu_an_2))[,3]))/(nboot+1)

length(which(boot_tu_evolN$intra_p<=as.data.frame(Anova(intra_tu_an_1))[,3]))/(nboot+1)

length(which(boot_tu_evolN$inter_p_TuReg<=as.data.frame(Anova(inter_tu_an_1))[1,3]))/(nboot+1)

length(which(boot_tu_evolN$inter_p_TeReg<=as.data.frame(Anova(inter_tu_an_1))[2,3]))/(nboot+1)

length(which(boot_tu_evolN$inter_p_int<=as.data.frame(Anova(inter_tu_an_1))[3,3]))/(nboot+1)

length(which(boot_te_evolN$lambda_p<=as.data.frame(Anova(gr_te_an_2))[,3]))/(nboot+1)

length(which(boot_te_evolN$intra_p<=as.data.frame(Anova(intra_te_an_1))[,3]))/(nboot+1)

length(which(boot_te_evolN$inter_p_TuReg<=as.data.frame(Anova(inter_te_an_1))[1,3]))/(nboot+1)

length(which(boot_te_evolN$inter_p_TeReg<=as.data.frame(Anova(inter_te_an_1))[2,3]))/(nboot+1)

length(which(boot_te_evolN$inter_p_int<=as.data.frame(Anova(inter_te_an_1))[3,3]))/(nboot+1)

hist(boot_tu_evolN$lambda_p)
abline(v=as.data.frame(Anova(gr_tu_an_2))[,3], col="red")

hist(boot_tu_evolN$intra_p)
abline(v=as.data.frame(Anova(intra_tu_an_1))[,3], col="red")

hist(boot_tu_evolN$inter_p_TuReg)
abline(v=as.data.frame(Anova(inter_tu_an_1))[1,3], col="red")

hist(boot_tu_evolN$inter_p_TeReg)
abline(v=as.data.frame(Anova(inter_tu_an_1))[2,3], col="red")

hist(boot_tu_evolN$inter_p_int)
abline(v=as.data.frame(Anova(inter_tu_an_1))[3,3], col="red")


hist(boot_te_evolN$lambda_p)
abline(v=as.data.frame(Anova(gr_te_an_2))[,3], col="red")

hist(boot_te_evolN$intra_p)
abline(v=as.data.frame(Anova(intra_te_an_1))[,3], col="red")

hist(boot_te_evolN$inter_p_TuReg)
abline(v=as.data.frame(Anova(inter_te_an_1))[1,3], col="red")

hist(boot_te_evolN$inter_p_TeReg)
abline(v=as.data.frame(Anova(inter_te_an_1))[2,3], col="red")

hist(boot_te_evolN$inter_p_int)
abline(v=as.data.frame(Anova(inter_te_an_1))[3,3], col="red")

as.data.frame(Anova(gr_tu_an_2))[,3]
as.data.frame(Anova(intra_tu_an_1))[,3]
as.data.frame(Anova(inter_tu_an_1))[1,3]
as.data.frame(Anova(inter_tu_an_1))[2,3]
as.data.frame(Anova(inter_tu_an_1))[3,3]
as.data.frame(Anova(gr_te_an_2))[,3]
as.data.frame(Anova(intra_te_an_1))[,3]
as.data.frame(Anova(inter_te_an_1))[1,3]
as.data.frame(Anova(inter_te_an_1))[2,3]
as.data.frame(Anova(inter_te_an_1))[3,3]


length(which(boot_tu_evolN$lambda_p<=0.05))/(nboot)
length(which(boot_tu_evolN$intra_p<=0.05))/(nboot)
length(which(boot_tu_evolN$inter_p_TuReg<=0.05))/(nboot)
length(which(boot_tu_evolN$inter_p_TeReg<=0.05))/(nboot)
length(which(boot_tu_evolN$inter_p_int<=0.05))/(nboot)
length(which(boot_te_evolN$lambda_p<=0.05))/(nboot)
length(which(boot_te_evolN$intra_p<=0.05))/(nboot)
length(which(boot_te_evolN$inter_p_TuReg<=0.05))/(nboot)
length(which(boot_te_evolN$inter_p_TeReg<=0.05))/(nboot)
length(which(boot_te_evolN$inter_p_int<=0.05))/(nboot)